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## Vershik, Anatoliĭ Moiseevich

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 Author ID: vershik.anatoli-m Published as: Vershik, A.; Vershik, A. M; Vershik, A. M.; Vershik, Anatol M.; Vershik, Anatoli; Vershik, Anatoli M.; Vershik, Anatolii; Vershik, Anatolii M.; Vershik, Anatolij; Vershik, Anatoly; Vershik, Anatoly M. Homepage: http://www.pdmi.ras.ru/~vershik External Links: MGP · Math-Net.Ru · Wikidata · ORCID · ResearchGate · dblp · GND
 Documents Indexed: 414 Publications since 1958, including 28 Books Biographic References: 3 Publications
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all top 5

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#### Fields

 98 Group theory and generalizations (20-XX) 78 Measure and integration (28-XX) 75 Combinatorics (05-XX) 75 Dynamical systems and ergodic theory (37-XX) 60 History and biography (01-XX) 59 Probability theory and stochastic processes (60-XX) 57 Topological groups, Lie groups (22-XX) 47 General and overarching topics; collections (00-XX) 44 Functional analysis (46-XX) 28 Number theory (11-XX) 26 Global analysis, analysis on manifolds (58-XX) 25 Operations research, mathematical programming (90-XX) 22 Calculus of variations and optimal control; optimization (49-XX) 21 Operator theory (47-XX) 21 Numerical analysis (65-XX) 21 Computer science (68-XX) 20 Quantum theory (81-XX) 19 Nonassociative rings and algebras (17-XX) 18 Differential geometry (53-XX) 17 General topology (54-XX) 15 Associative rings and algebras (16-XX) 15 Abstract harmonic analysis (43-XX) 14 Convex and discrete geometry (52-XX) 10 Statistical mechanics, structure of matter (82-XX) 8 Algebraic geometry (14-XX) 8 Manifolds and cell complexes (57-XX) 7 Partial differential equations (35-XX) 7 Mechanics of particles and systems (70-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Geometry (51-XX) 3 Order, lattices, ordered algebraic structures (06-XX) 3 $$K$$-theory (19-XX) 2 Mathematical logic and foundations (03-XX) 2 Real functions (26-XX) 2 Special functions (33-XX) 2 Approximations and expansions (41-XX) 2 Fluid mechanics (76-XX) 2 Relativity and gravitational theory (83-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Category theory; homological algebra (18-XX) 1 Functions of a complex variable (30-XX) 1 Potential theory (31-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral transforms, operational calculus (44-XX) 1 Algebraic topology (55-XX) 1 Biology and other natural sciences (92-XX) 1 Information and communication theory, circuits (94-XX)

#### Citations contained in zbMATH Open

278 Publications have been cited 2,965 times in 1,856 Documents Cited by Year
Random walks on discrete groups: Boundary and entropy. Zbl 0641.60009
Kaimanovich, V. A.; Vershik, A. M.
1983
Asymptotics of the Plancherel measure of the symmetric group and the limiting form of Young tableaux. Zbl 0406.05008
Vershik, A. M.; Kerov, S. V.
1977
Statistical mechanics of combinatorial partitions, and their limit shapes. Zbl 0868.05004
Vershik, A. M.
1996
Nonholonomic dynamical systems, geometry of distributions and variational problems. Zbl 0797.58007
Vershik, A. M.; Gershkovich, V. Ya.
1987
A new approach to representation theory of symmetric groups. Zbl 0959.20014
Okounkov, Andrei; Vershik, Anatoly
1996
Asymptotic theory of characters of the symmetric group. Zbl 0507.20006
Vershik, A. M.; Kerov, S. V.
1982
Characters and factor representations of the infinite symmetric group. Zbl 0534.20008
Vershik, A. M.; Kerov, S. V.
1981
Asymptotics of maximal and typical dimensions of irreducible representations of a symmetric group. Zbl 0592.20015
Vershik, A. M.; Kerov, S. V.
1985
Harmonic analysis on the infinite symmetric group. Zbl 1057.43005
Kerov, Sergei; Olshanski, Grigori; Vershik, Anatoly
2004
Characters and factor representations of the infinite unitary group. Zbl 0524.22017
Vershik, A. M.; Kerov, S. V.
1982
Representations of the group of diffeomorphisms. Zbl 0337.58003
Vershik, A. M.; Gel’fand, I. M.; Graev, M. I.
1975
Dynamic theory of growth in groups: Entropy, boundaries, examples. Zbl 0991.37005
Vershik, A. M.
2000
Harmonic analysis on the infinite symmetric group. A deformation of the regular representation. Zbl 0796.43005
Kerov, Serguei; Olshanski, Grigori; Vershik, Anatoli
1993
Limit measures arising in the asymptotic theory of symmetric groups. I. Zbl 0375.60007
Vershik, A. M.; Shmidt, A. A.
1977
Adic models of ergodic transformations, spectral theory, substitutions, and related topics. Zbl 0770.28013
Vershik, A. M.; Livshits, A. N.
1992
An infinite-dimensional analogue of the Lebesgue measure and distinguished properties of the gamma process. Zbl 0990.60053
Tsilevich, Natalia; Vershik, Anatoly; Yor, Marc
2001
$$C^*$$-algebras of irreversible dynamical systems. Zbl 1104.46037
Exel, R.; Vershik, A.
2006
Uniform algebraic approximation of shift and multiplication operators. Zbl 0484.47005
Vershik, A. M.
1981
Decreasing sequences of measurable partitions and their applications. Zbl 0238.28011
Vershik, A. M.
1970
Arithmetic construction of sofic partitions of hyperbolic toral automorphisms. Zbl 0915.58077
Kenyon, Richard; Vershik, Anatoly
1998
Ergodic unitarily invariant measures on the space of infinite Hermitian matrices. Zbl 0853.22016
Ol’shanskij, Grigorij; Vershik, Anatolij
1996
Nonfree actions of countable groups and their characters. Zbl 1279.37004
Vershik, A. M.
2011
The characters of the infinite symmetric group and probability properties of the Robinson-Schensted-Knuth algorithm. Zbl 0584.05004
Kerov, Sergei V.; Vershik, Anatol M.
1986
Description of invariant measures for the actions of some infinite- dimensional groups. Zbl 0324.28014
Vershik, A. M.
1974
Totally nonfree actions and the infinite symmetric group. Zbl 1294.37004
Vershik, A. M.
2012
Ergodic properties of the Erdős measure, the entropy of the goldenshift, and related problems. Zbl 0916.28012
Sidorov, Nikita; Vershik, Anatoly
1998
Reduction of nonholonomic variation problems to isoperimetric ones and connections in principal bundles. Zbl 0734.49023
Vershik, A. M.; Granichina, O. A.
1991
Long history of the Monge-Kantorovich transportation problem. Zbl 1284.01041
Vershik, A. M.
2013
Large deviations for integer partitions. Zbl 0972.60006
Dembo, A.; Vershik, A.; Zeitouni, O.
2000
A theorem on the Markov periodic approximation in ergodic theory. Zbl 0559.47006
Vershik, A. M.
1985
Representations of the group $$\text{SL}(2, R)$$, where $$R$$ is a ring of functions. Zbl 0288.22005
Vershik, A. M.; Gel’fand, I. M.; Graev, M. I.
1973
Differential geometry and Lagrangian mechanics with constraints. Zbl 0243.70014
Vershik, A. M.; Faddeev, L. D.
1972
Some isometry groups of the Urysohn space. Zbl 1108.54027
Cameron, P. J.; Vershik, A. M.
2006
The Kantorovich metric: the initial history and little-known applications. Zbl 1090.28009
Vershik, A. M.
2006
The universal Urysohn space, Gromov metric triples and random metrics on the natural numbers. Zbl 1005.53036
Vershik, A. M.
1998
Factorial representations of path groups. Zbl 0522.22013
Albeverio, Sergio; Høegh-Krohn, Raphael; Testard, Daniel; Vershik, A.
1983
$$BC$$-type interpolation Macdonald polynomials and binomial formula for Koornwinder polynomials. Zbl 0941.17005
Okounkov, Andrei; Vershik, Anatoly
1998
The limit shape of convex lattice polygons and related topics. Zbl 0848.52004
Vershik, A. M.
1994
Multivalued mappings with invariant measure (polymorphisms) and Markov operators. Zbl 0408.28014
Vershik, A. M.
1977
Lagrangian mechanics in invariant form. Zbl 0518.58015
Vershik, A. M.; Faddeev, L. D.
1975
Random metric spaces and universality. Zbl 1065.60005
Vershik, A. M.
2003
The Grothendieck group of infinite symmetric group and symmetric functions (with the elements of the theory of $$K_ 0$$-functor of AF- algebras). Zbl 0723.20005
Vershik, A. M.; Kerov, S. V.
1990
Representations of the group $$\text{SL}(2, R)$$, where $$R$$ is a ring of functions. Zbl 0297.22003
Vershik, A. M.; Gel’fand, I. M.; Graev, M. I.
1973
The word and geodesic problems in free solvable groups. Zbl 1207.20026
Myasnikov, A.; Roman’kov, V.; Ushakov, A.; Vershik, A.
2010
Linearly rigid metric spaces and the embedding problem. Zbl 1178.46016
Melleray, J.; Petrov, F. V.; Vershik, A. M.
2008
Locally semisimple algebras. Combinatorial theory and the $$K_ 0$$- functor. Zbl 0623.46036
Vershik, A. M.; Kerov, S. V.
1987
Amenability and approximation of infinite groups. Zbl 0533.22007
Vershik, A.
1982
Statistical properties of locally free groups with applications to braid groups and growth of random heaps. Zbl 1010.20056
Vershik, A. M.; Nechaev, S.; Bikbov, R.
2000
Does there exist a Lebesgue measure in the infinite-dimensional space? Zbl 1165.28003
Vershik, A. M.
2007
A new approach to the representation theory of symmetric groups. II. Zbl 1083.20502
Vershik, A. M.; Okoun’kov, A. Yu.
2005
On an infinite-dimensional group over a finite field. Zbl 1089.22006
Vershik, A. M.; Kerov, S. V.
1998
The theory of decreasing sequences of measurable partitions. Zbl 0853.28009
Vershik, A. M.
1994
Asymptotic behavior of the number of faces of random polyhedra and the neighborliness problem. Zbl 0791.52011
Vershik, A. M.; Sporyshev, P. V.
1992
On the number of convex lattice polytopes. Zbl 0772.52010
Bárány, I.; Vershik, A. M.
1992
The theorem about the periodic Markov approximation in ergodic theory. Zbl 0505.47006
Vershik, A. M.
1982
Some characteristic properties of Gaussian stochastic processes. Zbl 0141.15203
Vershik, A. M.
1965
The problem of describing central measures on the path spaces of graded graphs. Zbl 1370.37005
Vershik, A. M.
2014
Nonholonomic problems and the theory of distributions. Zbl 0666.58004
Vershik, A. M.; Gershkovich, V. Ya.
1988
Representations of the group of smooth mappings of a manifold $$X$$ into a compact Lie group. Zbl 0368.53034
Gelfand, I. M.; Graev, M. I.; Vershik, A. M.
1977
Geometry and dynamics of admissible metrics in measure spaces. Zbl 1261.37004
Vershik, Anatoly M.; Zatitskiy, Pavel B.; Petrov, Fedor V.
2013
Polymorphisms, Markov processes, and quasi-similarity. Zbl 1115.37002
Vershik, A. M.
2005
The limit shape and fluctuations of random partitions of naturals with fixed number of summands. Zbl 0996.05006
Vershik, A.; Yakubovich, Yu.
2001
Bijective arithmetic codings of hyperbolic automorphisms of the $$2$$-torus, and binary quadratic forms. Zbl 0949.37023
Sidorov, N.; Vershik, A.
1998
Continuum analogues of contragredient Lie algebras. (Lie algebras with a Cartan operator and nonlinear dynamical systems). Zbl 0691.17012
Savel’ev, M. V.; Vershik, A. M.
1989
Equipped graded graphs, projective limits of simplices, and their boundaries. Zbl 1323.05127
Vershik, A. M.
2015
Intrinsic metric on graded graphs, standardness, and invariant measures. Zbl 1336.28014
Vershik, A. M.
2014
Fock factorizations and decompositions of the $$L^ 2$$ spaces over general Lévy processes. Zbl 1060.46056
Vershik, A. M.; Tsilevich, N. V.
2003
Classification of measurable functions of several variables and invariantly distributed random matrices. Zbl 1025.28010
Vershik, A. M.
2002
Quasi-invariance du processus gamma et propriétés multiplicatives des distributions de Poisson-Dirichlet. Zbl 0938.60040
Tsilevich, Natalia; Vershik, Anatoly
1999
Asymptotic combinatorics and algebraic analysis. Zbl 0843.05003
Vershik, Anatoly M.
1995
Irreducible representations of the group $$G^X$$ and cohomologies. Zbl 0299.22004
Vershik, A. M.; Gel’fand, I. M.; Graev, M. I.
1974
Dynamics of metrics in measure spaces and their asymptotic invariants. Zbl 1203.37020
Vershik, A. M.
2010
Twisted Burnside theorem for type $$\text{II}_1$$ groups: an example. Zbl 1143.20026
Fel’shtyn, Alexander; Troitsky, Evgenij; Vershik, Anatoly
2006
A local limit theorem for random strict partitions. Zbl 0969.60034
Vershik, A. M.; Freĭman, G. A.; Yakubovich, Yu. V.
1999
Arithmetic isomorphism of hyperbolic toral automorphisms and sofic shifts. Zbl 0810.58031
Vershik, A. M.
1992
Nonholonomic manifolds and nilpotent analysis. Zbl 0693.53006
Gershkovich, V.; Vershik, A.
1988
Cohomology of groups in unitary representations, the neighborhood of the identity, and conditionally positive definite functions. Zbl 0528.43005
Vershik, A. M.; Karpushev, S. I.
1984
Frobenius-Schur functions (with an appendix by Vladimir Ivanov). Zbl 1051.05077
Olshanski, Grigori; Regev, Amitai; Vershik, Anatoly
2003
On the Markov-Krein identity and quasi-invariance of the gamma process. Zbl 1069.60046
Vershik, A.; Yor, M.; Tsilevich, N.
2001
Limit measures arising in the asymptotic theory of symmetric groups. II. Zbl 0423.60009
Vershik, A. M.; Shmidt, A. A.
1978
Some remarks on the infinite-dimensional problems of linear programming. Zbl 0224.90041
Vershik, A. M.
1970
Globalization of the partial isometries of metric spaces and local approximation of the group of isometries of Urysohn space. Zbl 1160.54020
Vershik, A. M.
2008
Limit distribution of the energy of a quantum ideal gas from the viewpoint of the theory of partitions of natural numbers. Zbl 0927.60089
Vershik, A. M.
1997
Random walks on braid groups: Brownian bridges, complexity and statistics. Zbl 0901.60010
Nechaev, S. K.; Grosberg, A. Yu.; Vershik, A. M.
1996
Local stationary algebras. Zbl 0810.16015
Vershik, A. M.
1991
Characters, factor representations and K-functor of the infinite symmetric group. Zbl 0545.22001
Kerov, S. V.; Vershik, A. M.
1984
A commutative model of presentation of the group of flows $$SL(2,R)^ X$$ that is connected with a unipotent subgroup. Zbl 0536.22008
Vershik, A. M.; Gel’fand, I. M.; Graev, M. I.
1983
Many-valued measure-preserving mappings (polymorphisms) and Markovian operators. Zbl 0517.28016
Vershik, A. M.
1983
Cohomology of groups in unitary representations, neighbourhood of the unit and conditionally positive definite functions. Zbl 0513.43009
Vershik, A. M.; Karpushev, S. I.
1982
Representations of the group of functions taking values in a compact Lie group. Zbl 0449.22019
Gelfand, I. M.; Graev, M. I.; Vershik, A. M.
1980
Probability measures in infinite-dimensional spaces. Zbl 0248.60007
Vershik, A. M.; Sudakov, V. N.
1969
Theorem on lacunary isomorphisms of monotonic sequences of partitions. Zbl 0186.20203
Vershik, A. M.
1968
Finite traces and representations of the group of infinite matrices over a finite field. Zbl 1286.22004
Gorin, Vadim; Kerov, Sergei; Vershik, Anatoly
2014
The Pascal automorphism has a continuous spectrum. Zbl 1271.37007
Vershik, A. M.
2011
Structure of the complementary series and special representations of the groups $$O(n,1)$$ and $$U(n,1)$$. Zbl 1148.22017
Vershik, A. M.; Graev, M. I.
2006
A random metric space is the universal Urysohn space. Zbl 1146.54309
Vershik, A. M.
2002
Examples of nonlinear continuous tensor products of measure spaces and non-Fock factorizations. Zbl 0912.46022
Tsirelson, B. S.; Vershik, A. M.
1998
The theory of filtrations of subalgebras, standardness, and independence. Zbl 1370.05220
Vershik, A. M.
2017
$$C^*$$-algebras associated with endomorphisms and polymorphisms of compact abelian groups. Zbl 1278.46050
Cuntz, Joachim; Vershik, Anatoly
2013
Dynamical systems, ergodic theory and applications. Edited by Ya. G. Sinai. Transl. from the Russian. 2nd, expanded and rev. ed. Zbl 1100.00500
Bunimovich, L. A.; Dani, S. G.; Dobrushin, R. L.; Jakobson, M. V.; Kornfeld, I. P.; Maslova, N. B.; Pesin, Ya. B.; Sinai, Ya. G.; Smillie, J.; Sukhov, Yu. M.; Vershik, A. M.
2000
Three theorems on the uniqueness of the Plancherel measure from different viewpoints. Zbl 1436.20020
Vershik, A. M.
2019
Asymptotics of the partition of the cube into Weyl simplices and an encoding of a Bernoulli scheme. Zbl 1427.37033
Vershik, A. M.
2019
The absolute of finitely generated groups. I: Commutative (semi)groups. Zbl 1403.28014
Vershik, Anatoly M.; Malyutin, Andrei V.
2018
The absolute of finitely generated groups. II: The Laplacian and degenerate parts. Zbl 07000556
Vershik, A. M.; Malyutin, A. V.
2018
Infinite geodesics in the discrete Heisenberg group. Zbl 1393.37047
Vershik, A. M.; Malyutin, A. V.
2018
The theory of filtrations of subalgebras, standardness, and independence. Zbl 1370.05220
Vershik, A. M.
2017
Universal adic approximation, invariant measures and scaled entropy. Zbl 1382.37009
Vershik, Anatolii M.; Zatitskii, Pavel B.
2017
Special representations of the Iwasawa subgroups of simple Lie groups. Zbl 1375.22010
Vershik, A. M.; Graev, M. I.
2017
On the relationship between combinatorial functions and representation theory. Zbl 1369.20013
Vershik, A. M.; Tsilevich, N. V.
2017
Equivalence of the Brownian and energy representations. Zbl 1360.22026
Albeverio, S.; Driver, B. K.; Gordina, Maria; Vershik, A. M.
2016
Cohomology of the Iwasawa subgroup of the group $$U(p,p)$$ in nonunitary representations. Zbl 1354.22019
Vershik, A. M.; Graev, M. I.
2016
Smoothness and standardness in the theory of $$AF$$-algebras and in the problem on invariant measures. Zbl 1388.22004
Vershik, A.
2016
Asymptotic theory of path spaces of graded graphs and its applications. Zbl 1409.37051
Vershik, Anatoly M.
2016
Equipped graded graphs, projective limits of simplices, and their boundaries. Zbl 1323.05127
Vershik, A. M.
2015
Phase transition in the exit boundary problem for random walks on groups. Zbl 1328.60117
Vershik, A. M.; Malyutin, A. V.
2015
Laplace operators on the cone of Radon measures. Zbl 1327.60105
Kondratiev, Yuri; Lytvynov, Eugene; Vershik, Anatoly
2015
Classification of finite metric spaces and combinatorics of convex polytopes. Zbl 1348.54021
Vershik, A. M.
2015
Several remarks on Pascal automorphism and infinite ergodic theory. Zbl 1344.37012
Vershik, Anatoly M.
2015
The serpentine representation of the infinite symmetric group and the basic representation of the affine Lie algebra $$\widehat{\mathfrak{sl}_2}$$. Zbl 1319.20011
Tsilevich, Natalia V.; Vershik, Anatoly M.
2015
Standardness as an invariant formulation of independence. Zbl 1383.28001
Vershik, A. M.
2015
The problem of describing central measures on the path spaces of graded graphs. Zbl 1370.37005
Vershik, A. M.
2014
Intrinsic metric on graded graphs, standardness, and invariant measures. Zbl 1336.28014
Vershik, A. M.
2014
Finite traces and representations of the group of infinite matrices over a finite field. Zbl 1286.22004
Gorin, Vadim; Kerov, Sergei; Vershik, Anatoly
2014
Infinite-dimensional Schur-Weyl duality and the Coxeter-Laplace operator. Zbl 1306.20007
Tsilevich, N. V.; Vershik, A. M.
2014
A few snapshots from the work of Mikhail Gromov. Zbl 1317.01017
Burago, D.; Eliashberg, Y.; Bestvina, M.; Forstnerič, F.; Guth, L.; Nabutovsky, A.; Phillips, A.; Roe, J.; Vershik, A.
2014
Cohomology in nonunitary representations of semisimple Lie groups (the group $$U(2,2)$$). Zbl 1317.22011
Vershik, A. M.; Graev, M. I.
2014
Virtual continuity of measurable functions and its applications. Zbl 1320.28003
Vershik, A. M.; Zatitskiy, P. B.; Petrov, F. V.
2014
Nonsingular transformations of symmetric Lévy processes. Zbl 1317.60057
Vershik, A. M.; Smorodina, N. V.
2014
Two ways to define compatible metrics on the simplex of measures. Zbl 1319.46024
Vershik, A. M.
2014
Long history of the Monge-Kantorovich transportation problem. Zbl 1284.01041
Vershik, A. M.
2013
Geometry and dynamics of admissible metrics in measure spaces. Zbl 1261.37004
Vershik, Anatoly M.; Zatitskiy, Pavel B.; Petrov, Fedor V.
2013
$$C^*$$-algebras associated with endomorphisms and polymorphisms of compact abelian groups. Zbl 1278.46050
Cuntz, Joachim; Vershik, Anatoly
2013
Virtual continuity of measurable functions of several variables and embedding theorems. Zbl 1305.28004
Vershik, A. M.; Zatitskiy, P. B.; Petrov, F. V.
2013
On classification of measurable functions of several variables. Zbl 1388.28003
Vershik, A. M.
2013
Special representations of nilpotent Lie groups and the associated Poisson representations of current groups. Zbl 1298.22006
Vershik, Anatoly M.; Graev, Mark I.
2013
Totally nonfree actions and the infinite symmetric group. Zbl 1294.37004
Vershik, A. M.
2012
Scaling entropy and automorphisms with pure point spectrum. Zbl 1251.37009
Vershik, A. M.
2012
Special representations of the groups $$U(\infty,1)$$ and $$O(\infty,1)$$ and the associated representations of the current groups $$U(\infty,1)^X$$ and $$O(\infty,1)^X$$ in quasi-Poisson spaces. Zbl 1279.22032
Vershik, A. M.; Graev, M. I.
2012
The Poisson model of the Fock space and representations of current groups. Zbl 1256.81058
Vershik, A. M.; Graev, M. I.
2012
Leonid Vital’evich Kantorovich (on the 100th anniversary of his birth). Zbl 1253.01043
Vershik, A. M.; Kutateladze, S. S.; Novikov, S. P.
2012
Nonfree actions of countable groups and their characters. Zbl 1279.37004
Vershik, A. M.
2011
The Pascal automorphism has a continuous spectrum. Zbl 1271.37007
Vershik, A. M.
2011
Description of the characters and factor representations of the infinite symmetric inverse semigroup. Zbl 1271.20072
Vershik, A. M.; Nikitin, P. P.
2011
The word and geodesic problems in free solvable groups. Zbl 1207.20026
Myasnikov, A.; Roman’kov, V.; Ushakov, A.; Vershik, A.
2010
Dynamics of metrics in measure spaces and their asymptotic invariants. Zbl 1203.37020
Vershik, A. M.
2010
Uncountable graphs and invariant measures on the set of universal countable graphs. Zbl 1209.05158
Petrov, Fedor; Vershik, Anatoly
2010
Numerical experiments in problems of asymptotic representation theory. Zbl 1288.20012
Vershik, A.; Pavlov, D.
2010
Orbit theory, locally finite permutations and Morse arithmetic. Zbl 1217.37002
Vershik, A. M.
2010
Integral models of representations of the current groups of simple Lie groups. Zbl 1202.22019
Vershik, A. M.; Graev, M. I.
2009
The adic realization of the Morse transformation and the extension of its action to the solenoid. Zbl 1303.37004
Vershik, A. M.; Solomyak, B.
2009
Linearly rigid metric spaces and the embedding problem. Zbl 1178.46016
Melleray, J.; Petrov, F. V.; Vershik, A. M.
2008
Globalization of the partial isometries of metric spaces and local approximation of the group of isometries of Urysohn space. Zbl 1160.54020
Vershik, A. M.
2008
Scaled entropy of filtrations of $$\sigma$$-fields. Zbl 1161.28005
Vershik, A. M.; Gorbulsky, A. D.
2008
Integral models of representations of current groups. Zbl 1162.22019
Vershik, A. M.; Graev, M. I.
2008
Algebraic polymorphisms. Zbl 1154.37304
Schmidt, Klaus; Vershik, Anatoly
2008
Invariant measures for the continual Cartan subgroup. Zbl 1187.37007
Vershik, A. M.
2008
The behavior of the Laplace transform of the invariant measure on the hypersphere of high dimension. Zbl 1178.58010
Vershik, A. M.
2008
A new approach to the representation theory of the symmetric groups. IV: $$\mathbb{Z}_2$$-graded groups and algebras; projective representations of the group $$S_n$$. Zbl 1196.20017
Vershik, A. M.; Sergeev, A. N.
2008
The local stationary presentation of the alternating groups and the normal form. Zbl 1150.20001
Vershik, A.; Vsemirnov, M.
2008
Integral models of unitary representations of current groups with values in semidirect products. Zbl 1162.22020
Vershik, A. M.; Graev, M. I.
2008
Representation theory, dynamical systems, combinatorial methods. Part 16. Zbl 1170.49302
Vershik, A. M. (ed.); Tsilevich, N. V. (ed.)
2008
Boundaries of braid groups and the Markov-Ivanovsky normal form. Zbl 1155.60033
Vershik, A. M.; Malyutin, A. V.
2008
Does there exist a Lebesgue measure in the infinite-dimensional space? Zbl 1165.28003
Vershik, A. M.
2007
Induced representations of the infinite symmetric group. Zbl 1153.20008
Tsilevich, N. V.; Vershik, A. M.
2007
Krein duality, positive 2-algebras, and the dilation of comultiplications. Zbl 1184.16034
Vershik, A. M.
2007
Markov measures on Young tableaux and induced representations of the infinite symmetric group. Zbl 1155.20013
Vershik, A. M.; Tsilevich, N. V.
2007
Induced representations of the infinite symmetric group and their spectral theory. Zbl 1327.20010
Vershik, A. M.; Tsilevich, N. V.
2007
Representation theory, dynamical systems, combinatorial methods. Part 15. Transl. from the Russian. Zbl 1136.49301
Vershik, A. M. (ed.); Tsilevich, N. V. (ed.)
2007
Linearly rigid metric spaces. Zbl 1121.54043
Melleray, Julien; Petrov, Fedor; Vershik, Anatoly
2007
What is good for mathematics? Thoughts on the Clay Millennium Prizes. Zbl 1128.01314
Vershik, Anatoly
2007
$$C^*$$-algebras of irreversible dynamical systems. Zbl 1104.46037
Exel, R.; Vershik, A.
2006
Some isometry groups of the Urysohn space. Zbl 1108.54027
Cameron, P. J.; Vershik, A. M.
2006
The Kantorovich metric: the initial history and little-known applications. Zbl 1090.28009
Vershik, A. M.
2006
Twisted Burnside theorem for type $$\text{II}_1$$ groups: an example. Zbl 1143.20026
Fel’shtyn, Alexander; Troitsky, Evgenij; Vershik, Anatoly
2006
Structure of the complementary series and special representations of the groups $$O(n,1)$$ and $$U(n,1)$$. Zbl 1148.22017
Vershik, A. M.; Graev, M. I.
2006
On different models of representations of the infinite symmetric group. Zbl 1149.20013
Tsilevich, N. V.; Vershik, A. M.
2006
Fluctuations of the maximal particle energy of the quantum ideal gas and random partitions. Zbl 1113.82010
Vershik, A.; Yakubovich, Yu.
2006
What does a generic Markov operator look like? Zbl 1173.47306
Vershik, A. M.
2006
Traces on infinite-dimensional Brauer algebras. Zbl 1137.20011
Nikitin, P. P.; Vershik, A. M.
2006
Compactness of the congruence group of measurable functions in several variables. Zbl 1127.28001
Vershik, A. M.; Haböck, U.
2006
Gelfand-Tsetlin algebras, expectations, inverse limits, Fourier analysis. Zbl 1101.22002
Vershik, A. M.
2006
Universality and randomness for the graphs and metric spaces. Zbl 1134.05098
Vershik, A. M.
2006
A new approach to the representation theory of symmetric groups. II. Zbl 1083.20502
Vershik, A. M.; Okoun’kov, A. Yu.
2005
Polymorphisms, Markov processes, and quasi-similarity. Zbl 1115.37002
Vershik, A. M.
2005
The basic representation of the current group $$O(n,1)^X$$ in the $$L^2$$ space over the generalized Lebesgue measure. Zbl 1147.22013
Graev, M. I.; Vershik, A. M.
2005
A commutative model of a representation of the group $$O(n, 1)^{X}$$ and a generalized Lebesgue measure in the space of distributions. Zbl 1135.22018
Graev, M. I.; Vershik, A. M.
2005
Geometrical approach to the free solvable groups. Zbl 1104.20034
Vershik, A. M.; Dobrynin, S. V.
2005
On the Fourier transform on the infinite symmetric group. Zbl 1078.43002
Vershik, A. M.; Tsilevich, N. V.
2005
Harmonic analysis on the infinite symmetric group. Zbl 1057.43005
Kerov, Sergei; Olshanski, Grigori; Vershik, Anatoly
2004
Random and universal metric spaces. Zbl 1124.28012
Vershik, Anatoly M.
2004
Ol’ga Aleksandrovna Ladyzhenskaya (obituary). Zbl 1062.01503
Arnol’d, V. I.; Birman, M. Sh.; Vershik, A. M.; et al.
2004
Random metric spaces and universality. Zbl 1065.60005
Vershik, A. M.
2003
Fock factorizations and decompositions of the $$L^ 2$$ spaces over general Lévy processes. Zbl 1060.46056
Vershik, A. M.; Tsilevich, N. V.
2003
Frobenius-Schur functions (with an appendix by Vladimir Ivanov). Zbl 1051.05077
Olshanski, Grigori; Regev, Amitai; Vershik, Anatoly
2003
Two lectures on the asymptotic representation theory and statistics of Young diagrams. Zbl 1035.05101
Vershik, A.
2003
Asymptotics of the uniform measure on simplices, and random compositions and partitions. Zbl 1081.60009
Vershik, A. M.; Yakubovich, Yu. V.
2003
Canonical semigroups of states and cocycles for the group of automorphisms of a homogeneous tree. Zbl 1031.43004
Kuhn, G.; Vershik, A.
2003
Kolmogorov’s example (A survey of actions of infinite-dimensional groups with an invariant probability measure). Zbl 1055.37006
Vershik, A. M.
2003
Asymptotic combinatorics with applications to mathematical physics. A European mathematical summer school held at the Euler Institute, St. Petersburg, Russia, July 9–20, 2001. Zbl 1014.00010
Vershik, A. M. (ed.)
2003
Strange factor representations of type II$$_1$$ and pairs of dual dynamical systems. Zbl 1059.46041
Vershik, A. M.
2003
...and 178 more Documents
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#### Cited by 1,836 Authors

 109 Vershik, Anatoliĭ Moiseevich 41 Maslov, Viktor Pavlovich 29 Ol’shanskiĭ, Grigoriĭ Iosifovich 26 Borodin, Alexei 22 Kerov, Sergei V. 20 Neretin, Yuriĭ Aleksandrovich 18 Albeverio, Sergio A. 16 Kaimanovich, Vadim A. 16 Petrov, Fedor Vladimirovich 13 Graev, Mark Iosifovich 13 Lytvynov, Eugene W. 13 Tsilevich, Natalia V. 12 Bufetov, Aleksandr Igorevich 12 Gorin, Vadim 12 Zatitskii, Pavel B. 11 Bufetov, Alekseĭ Igor’evich 11 Erschler, Anna 11 Grigorchuk, Rostislav Ivanovich 10 Kondrat’yev, Yuriĭ Grygorovych 10 Nazaikinskii, Vladimir E. 10 Pak, Igor 10 Peres, Yuval 10 Sachkov, Yuriĭ Leonidovich 10 Solomyak, Boris 9 Petrov, Leonid 9 Ryzhikov, Valeriĭ Valentinovich 9 Śniady, Piotr 9 Woess, Wolfgang 8 Berestovskiĭ, Valeriĭ Nikolaevich 8 Bogolyubov, Nikolaĭ Mikhaĭlovich 8 Fel’shtyn, Alexander 8 Okun’kov, Andreĭ Yur’evich 8 Regev, Amitai 8 Sidorov, Nikita A. 8 Tamuz, Omer 8 Troitskiĭ, Evgeniĭ Vadimovich 7 Agrachev, Andreĭ Aleksandrovich 7 Bogachev, Leonid V. 7 Diaconis, Persi Warren 7 Feldman, Jacob 7 Granovsky, Boris L. 7 Hartman, Yair 7 Kirillov, Anatol N. 7 Minabutdinov, A. R. 7 Myasnikov, Alexei G. 7 Panova, Greta 7 Strahov, Eugene 7 Ushakov, Alexander S. 7 Yor, Marc 6 Berthé, Valérie 6 Björklund, Michael 6 Bowen, Lewis Phylip 6 Daletskii, Alexei 6 Dudko, Artem 6 Ferenczi, Sébastien 6 Fomin, Sergey Vladimirovich 6 Gnedin, Alexander V. 6 Grigoryan, Suren Arshakovich 6 Høegh-Krohn, Raphael J. 6 Hołubowski, Waldemar 6 Kabluchko, Zakhar A. 6 Kapovich, Ilya 6 Mairesse, Jean 6 Rains, Eric M. 6 Sakbaev, Vsevolod Zhanovich 6 Schmidt, Klaus 6 Smorodina, Natal’ya Vasil’evna 6 Yakubovich, Yuri V. 5 Bárány, Imre 5 Brieussel, Jérémie 5 de León Rodríguez, Manuel 5 Fulman, Jason E. 5 Goodman, Frederick M. 5 Kalantar, Mehrdad 5 Kosyak, Alexandre V. 5 Kuznetsova, Alla. Yu. 5 Lijoi, Antonio 5 Malyutin, Andrei Valer’evich 5 Marsden, Jerrold Eldon 5 Mathéus, Frédéric 5 Melleray, Julien 5 Molchanov, Vladimir Fedorovich 5 Nešetřil, Jaroslav 5 Nessonov, Nikolai I. 5 Nikitin, Pavel P. 5 Petersen, Karl E. 5 Pitman, Jim William 5 Pittel, Boris G. 5 Raeburn, Iain 5 Ram, Arun 5 Siegel, Anne 5 Sinaĭ, Yakov Grigor’evich 5 Sirvent, Víctor F. 5 Słowik, Roksana 5 Stammeier, Nicolai 5 Thuswaldner, Jörg Maximilian 5 Tsirelson, Boris 5 Varjú, Péter Pál 5 Veselov, Alexander Petrovich 4 Abbes, Samy ...and 1,736 more Authors
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#### Cited in 322 Serials

 138 Journal of Mathematical Sciences (New York) 79 Functional Analysis and its Applications 58 Journal of Functional Analysis 55 Advances in Mathematics 51 The Annals of Probability 43 Mathematical Notes 43 Journal of Algebra 41 Transactions of the American Mathematical Society 40 Israel Journal of Mathematics 34 Journal of Soviet Mathematics 30 Journal of Mathematical Physics 30 Siberian Mathematical Journal 29 Ergodic Theory and Dynamical Systems 29 Probability Theory and Related Fields 26 Proceedings of the American Mathematical Society 25 Communications in Mathematical Physics 22 Advances in Applied Mathematics 21 Journal of Geometry and Physics 21 Russian Journal of Mathematical Physics 19 Annales de l’Institut Fourier 18 Duke Mathematical Journal 18 Topology and its Applications 17 Journal of Combinatorial Theory. Series A 16 Theoretical and Mathematical Physics 16 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 16 Journal of Algebraic Combinatorics 16 Journal of Dynamical and Control Systems 15 Discrete Mathematics 15 Journal of Statistical Physics 15 Inventiones Mathematicae 14 Stochastic Processes and their Applications 13 Monatshefte für Mathematik 13 European Journal of Combinatorics 12 Journal d’Analyse Mathématique 11 Journal of Mathematical Analysis and Applications 11 Letters in Mathematical Physics 11 Discrete & Computational Geometry 11 The Annals of Applied Probability 11 International Journal of Algebra and Computation 11 Linear Algebra and its Applications 11 Russian Mathematics 10 Mathematische Zeitschrift 10 Acta Applicandae Mathematicae 10 Journal of Theoretical Probability 10 Geometric and Functional Analysis. GAFA 10 Bulletin of the American Mathematical Society. New Series 10 Infinite Dimensional Analysis, Quantum Probability and Related Topics 9 Reports on Mathematical Physics 9 Russian Mathematical Surveys 9 Compositio Mathematica 9 Random Structures & Algorithms 9 St. Petersburg Mathematical Journal 8 Communications in Algebra 8 Journal of Differential Equations 8 Bernoulli 8 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 8 Algebras and Representation Theory 8 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 8 Groups, Geometry, and Dynamics 7 Geometriae Dedicata 7 Mathematische Annalen 7 International Journal of Mathematics 7 Selecta Mathematica. New Series 7 Annals of Mathematics. Second Series 7 Comptes Rendus. Mathématique. Académie des Sciences, Paris 7 Proceedings of the Steklov Institute of Mathematics 6 Theoretical Computer Science 6 Statistics & Probability Letters 6 Vestnik St. Petersburg University. Mathematics 6 Electronic Journal of Probability 6 Discrete and Continuous Dynamical Systems 6 Journal of High Energy Physics 5 Reviews in Mathematical Physics 5 The Mathematical Intelligencer 5 Integral Equations and Operator Theory 5 Journal of Multivariate Analysis 5 Annals of Pure and Applied Logic 5 Differential Geometry and its Applications 5 Indagationes Mathematicae. New Series 5 SIAM Journal on Optimization 5 Combinatorics, Probability and Computing 5 Doklady Mathematics 4 Nonlinearity 4 Nuclear Physics. B 4 Theory of Probability and its Applications 4 Journal of Number Theory 4 Nagoya Mathematical Journal 4 Publications of the Research Institute for Mathematical Sciences, Kyoto University 4 Systems & Control Letters 4 Journal of the American Mathematical Society 4 Sbornik: Mathematics 4 Dynamical Systems 4 Journal of Modern Dynamics 4 Carpathian Mathematical Publications 4 Arnold Mathematical Journal 3 Advances in Applied Probability 3 Archive for Rational Mechanics and Analysis 3 Communications on Pure and Applied Mathematics 3 Discrete Applied Mathematics 3 International Journal of Theoretical Physics ...and 222 more Serials
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#### Cited in 60 Fields

 582 Probability theory and stochastic processes (60-XX) 377 Group theory and generalizations (20-XX) 362 Combinatorics (05-XX) 339 Dynamical systems and ergodic theory (37-XX) 222 Topological groups, Lie groups (22-XX) 190 Measure and integration (28-XX) 164 Functional analysis (46-XX) 131 Abstract harmonic analysis (43-XX) 128 Statistical mechanics, structure of matter (82-XX) 118 Differential geometry (53-XX) 99 Number theory (11-XX) 93 Global analysis, analysis on manifolds (58-XX) 87 Quantum theory (81-XX) 67 Operator theory (47-XX) 67 Convex and discrete geometry (52-XX) 66 General topology (54-XX) 64 Computer science (68-XX) 55 Mechanics of particles and systems (70-XX) 54 Nonassociative rings and algebras (17-XX) 51 Partial differential equations (35-XX) 46 Associative rings and algebras (16-XX) 46 Statistics (62-XX) 43 Special functions (33-XX) 42 Calculus of variations and optimal control; optimization (49-XX) 39 Linear and multilinear algebra; matrix theory (15-XX) 39 Manifolds and cell complexes (57-XX) 38 Mathematical logic and foundations (03-XX) 25 Operations research, mathematical programming (90-XX) 24 Systems theory; control (93-XX) 23 Algebraic geometry (14-XX) 23 Numerical analysis (65-XX) 22 Information and communication theory, circuits (94-XX) 20 Potential theory (31-XX) 17 History and biography (01-XX) 17 Geometry (51-XX) 17 Fluid mechanics (76-XX) 16 Order, lattices, ordered algebraic structures (06-XX) 15 Algebraic topology (55-XX) 14 Functions of a complex variable (30-XX) 14 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 13 Harmonic analysis on Euclidean spaces (42-XX) 11 Several complex variables and analytic spaces (32-XX) 11 Ordinary differential equations (34-XX) 10 Biology and other natural sciences (92-XX) 9 Approximations and expansions (41-XX) 7 Category theory; homological algebra (18-XX) 6 $$K$$-theory (19-XX) 6 Real functions (26-XX) 6 Difference and functional equations (39-XX) 6 Integral equations (45-XX) 6 Classical thermodynamics, heat transfer (80-XX) 5 General and overarching topics; collections (00-XX) 5 Integral transforms, operational calculus (44-XX) 4 Commutative algebra (13-XX) 4 Relativity and gravitational theory (83-XX) 3 General algebraic systems (08-XX) 2 Sequences, series, summability (40-XX) 2 Optics, electromagnetic theory (78-XX) 2 Mathematics education (97-XX) 1 Mechanics of deformable solids (74-XX)

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