Vershik, Anatolii M.; Veprev, Georgii A.; Zatitskii, Pavel B. Dynamics of metrics in measure spaces and scaling entropy. (English. Russian original) Zbl 07794496 Russ. Math. Surv. 78, No. 3, 443-499 (2023); translation from Usp. Mat. Nauk 78, No. 3, 53-114 (2023). MSC: 28C15 28D05 37A05 37A35 PDFBibTeX XMLCite \textit{A. M. Vershik} et al., Russ. Math. Surv. 78, No. 3, 443--499 (2023; Zbl 07794496); translation from Usp. Mat. Nauk 78, No. 3, 53--114 (2023) Full Text: DOI arXiv MNR
Vershik, Anatoly M.; Petrov, Fedor V. Central measures of continuous graded graphs: the case of distinct frequencies. (English) Zbl 1503.05087 Eur. J. Math. 8, Suppl. 2, S481-S493 (2022). MSC: 05C63 05C80 28C15 PDFBibTeX XMLCite \textit{A. M. Vershik} and \textit{F. V. Petrov}, Eur. J. Math. 8, S481--S493 (2022; Zbl 1503.05087) Full Text: DOI arXiv
Vershik, A. M.; Tsilevich, N. V. Ergodicity and totality of partitions associated with the RSK correspondence. (English. Russian original) Zbl 1475.05171 Funct. Anal. Appl. 55, No. 1, 26-33 (2021); translation from Funkts. Anal. Prilozh. 55, No. 1, 33-42 (2021). MSC: 05E10 28D05 60C05 PDFBibTeX XMLCite \textit{A. M. Vershik} and \textit{N. V. Tsilevich}, Funct. Anal. Appl. 55, No. 1, 26--33 (2021; Zbl 1475.05171); translation from Funkts. Anal. Prilozh. 55, No. 1, 33--42 (2021) Full Text: DOI arXiv
Vershik, A. M.; Zatitskii, P. B. On a universal Borel adic space. (English. Russian original) Zbl 1435.28017 J. Math. Sci., New York 240, No. 5, 515-524 (2019); translation from Zap. Nauchn. Semin. POMI 468, 24-38 (2018). MSC: 28C15 05C90 28D05 PDFBibTeX XMLCite \textit{A. M. Vershik} and \textit{P. B. Zatitskii}, J. Math. Sci., New York 240, No. 5, 515--524 (2019; Zbl 1435.28017); translation from Zap. Nauchn. Semin. POMI 468, 24--38 (2018) Full Text: DOI arXiv
Vershik, A. M. Duality and free measures in vector spaces, the spectral theory of actions of non-locally compact groups. (English) Zbl 1429.46031 J. Math. Sci., New York 238, No. 4, 390-405 (2019) and Zap. Nauchn. Semin. POMI 457, 74-100 (2017). Reviewer: Hans Weber (Udine) MSC: 46G12 28C20 PDFBibTeX XMLCite \textit{A. M. Vershik}, J. Math. Sci., New York 238, No. 4, 390--405 (2019; Zbl 1429.46031) Full Text: DOI arXiv
Vershik, A. M.; Zatitskiy, Pavel B. Combinatorial invariants of metric filtrations and automorphisms; the universal adic graph. (English. Russian original) Zbl 1418.28001 Funct. Anal. Appl. 52, No. 4, 258-269 (2018); translation from Funkts. Anal. Prilozh. 52, No. 4, 23-37 (2018). MSC: 28C15 05C90 28D05 PDFBibTeX XMLCite \textit{A. M. Vershik} and \textit{P. B. Zatitskiy}, Funct. Anal. Appl. 52, No. 4, 258--269 (2018; Zbl 1418.28001); translation from Funkts. Anal. Prilozh. 52, No. 4, 23--37 (2018) Full Text: DOI arXiv
Vershik, Anatoly M.; Malyutin, Andrei V. The absolute of finitely generated groups. I: Commutative (semi)groups. (English) Zbl 1403.28014 Eur. J. Math. 4, No. 4, 1476-1490 (2018). MSC: 28C10 31C35 42C20 60J05 PDFBibTeX XMLCite \textit{A. M. Vershik} and \textit{A. V. Malyutin}, Eur. J. Math. 4, No. 4, 1476--1490 (2018; Zbl 1403.28014) Full Text: DOI arXiv
Vershik, Anatolii M.; Zatitskii, Pavel B. Universal adic approximation, invariant measures and scaled entropy. (English. Russian original) Zbl 1382.37009 Izv. Math. 81, No. 4, 734-770 (2017); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 81, No. 4, 68-107 (2017). Reviewer: Sophia L. Kalpazidou (Thessaloniki) MSC: 37B10 37A35 37A50 28D20 PDFBibTeX XMLCite \textit{A. M. Vershik} and \textit{P. B. Zatitskii}, Izv. Math. 81, No. 4, 734--770 (2017; Zbl 1382.37009); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 81, No. 4, 68--107 (2017) Full Text: DOI arXiv
Vershik, A. M.; Haböck, Ulrich On the classification problem of measurable functions in several variables and on matrix distributions. (English) Zbl 1379.37008 J. Math. Sci., New York 219, No. 5, 683-699 (2016) and Zap. Nauchn. Semin. POMI 441, 119-143 (2015). MSC: 37A30 28D05 28A20 28A33 PDFBibTeX XMLCite \textit{A. M. Vershik} and \textit{U. Haböck}, J. Math. Sci., New York 219, No. 5, 683--699 (2016; Zbl 1379.37008) Full Text: DOI
Vershik, A. M.; Zatitskiĭ, P. B.; Petrov, F. V. Integration of virtually continuous functions over bistochastic measures and the trace formula for nuclear operators. (English. Russian original) Zbl 1345.28001 St. Petersbg. Math. J. 27, No. 3, 393-398 (2016); translation from Algebra Anal. 27, No. 3, 66-74 (2015). Reviewer: Olga Maleva (Birmingham) MSC: 28A25 PDFBibTeX XMLCite \textit{A. M. Vershik} et al., St. Petersbg. Math. J. 27, No. 3, 393--398 (2016; Zbl 1345.28001); translation from Algebra Anal. 27, No. 3, 66--74 (2015) Full Text: DOI Link
Vershik, A. M. Standardness as an invariant formulation of independence. (English. Russian original) Zbl 1383.28001 Funct. Anal. Appl. 49, No. 4, 253-263 (2015); translation from Funkts. Anal. Prilozh. 49, No. 4, 18-32 (2015). MSC: 28A05 PDFBibTeX XMLCite \textit{A. M. Vershik}, Funct. Anal. Appl. 49, No. 4, 253--263 (2015; Zbl 1383.28001); translation from Funkts. Anal. Prilozh. 49, No. 4, 18--32 (2015) Full Text: DOI arXiv
Vershik, Anatoly M. Several remarks on Pascal automorphism and infinite ergodic theory. (English) Zbl 1344.37012 Armen. J. Math. 7, No. 2, 85-96 (2015). MSC: 37A40 28D05 60G50 PDFBibTeX XMLCite \textit{A. M. Vershik}, Armen. J. Math. 7, No. 2, 85--96 (2015; Zbl 1344.37012) Full Text: arXiv
Vershik, A. M.; Zatitskiy, P. B.; Petrov, F. V. Virtual continuity of measurable functions and its applications. (English. Russian original) Zbl 1320.28003 Russ. Math. Surv. 69, No. 6, 1031-1063 (2014); translation from Usp. Mat. Nauk 69, No. 6, 81-114 (2014). Reviewer: K. P. Hart (Delft) MSC: 28A20 26B05 46E35 54E35 PDFBibTeX XMLCite \textit{A. M. Vershik} et al., Russ. Math. Surv. 69, No. 6, 1031--1063 (2014; Zbl 1320.28003); translation from Usp. Mat. Nauk 69, No. 6, 81--114 (2014) Full Text: DOI arXiv
Vershik, A. M. The problem of describing central measures on the path spaces of graded graphs. (English. Russian original) Zbl 1370.37005 Funct. Anal. Appl. 48, No. 4, 256-271 (2014); translation from Funkts. Anal. Prilozh. 48, No. 4, 26-46 (2014). MSC: 37A05 28D05 46A55 PDFBibTeX XMLCite \textit{A. M. Vershik}, Funct. Anal. Appl. 48, No. 4, 256--271 (2014; Zbl 1370.37005); translation from Funkts. Anal. Prilozh. 48, No. 4, 26--46 (2014) Full Text: DOI arXiv
Vershik, A. M. Intrinsic metric on graded graphs, standardness, and invariant measures. (English) Zbl 1336.28014 J. Math. Sci., New York 200, No. 6, 677-681 (2014) and Zap. Nauchn. Semin. POMI 421, 58-67 (2014). MSC: 28D99 28C10 PDFBibTeX XMLCite \textit{A. M. Vershik}, J. Math. Sci., New York 200, No. 6, 677--681 (2014; Zbl 1336.28014) Full Text: DOI arXiv
Vershik, A. M.; Zatitskiy, P. B.; Petrov, F. V. Virtual continuity of measurable functions of several variables and embedding theorems. (English. Russian original) Zbl 1305.28004 Funct. Anal. Appl. 47, No. 3, 165-173 (2013); translation from Funkts. Anal. Prilozh. 47, No. 3, 1-11 (2013). MSC: 28A20 26B05 46E35 PDFBibTeX XMLCite \textit{A. M. Vershik} et al., Funct. Anal. Appl. 47, No. 3, 165--173 (2013; Zbl 1305.28004); translation from Funkts. Anal. Prilozh. 47, No. 3, 1--11 (2013) Full Text: DOI arXiv
Vershik, A. M. On classification of measurable functions of several variables. (English. Russian original) Zbl 1388.28003 J. Math. Sci., New York 190, No. 3, 427-437 (2013); translation from Zap. Nauchn. Semin. POMI 403, 35-57 (2012). MSC: 28A20 60B20 PDFBibTeX XMLCite \textit{A. M. Vershik}, J. Math. Sci., New York 190, No. 3, 427--437 (2013; Zbl 1388.28003); translation from Zap. Nauchn. Semin. POMI 403, 35--57 (2012) Full Text: DOI arXiv
Vershik, A. M. Scaling entropy and automorphisms with pure point spectrum. (English. Russian original) Zbl 1251.37009 St. Petersbg. Math. J. 23, No. 1, 75-91 (2012); translation from Algebra Anal. 23, No. 1, 111-135 (2011). Reviewer: el Houcein el Abdalaoui (Saint Etienne du Rouvray) MSC: 37A35 28D05 PDFBibTeX XMLCite \textit{A. M. Vershik}, St. Petersbg. Math. J. 23, No. 1, 75--91 (2012; Zbl 1251.37009); translation from Algebra Anal. 23, No. 1, 111--135 (2011) Full Text: DOI arXiv
Vershik, A. M. Orbit theory, locally finite permutations and Morse arithmetic. (English) Zbl 1217.37002 Kolyada, Sergiy (ed.) et al., Dynamical numbers. Interplay between dynamical systems and number theory. A special program, May 1–July 31, 2009. International conference, MPI, Bonn, Germany, July 20–24, 2009. Proceedings. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4958-3). Contemporary Mathematics 532, 115-136 (2010). MSC: 37A20 28D05 PDFBibTeX XMLCite \textit{A. M. Vershik}, Contemp. Math. 532, 115--136 (2010; Zbl 1217.37002) Full Text: arXiv
Vershik, A. M. Dynamics of metrics in measure spaces and their asymptotic invariants. (English) Zbl 1203.37020 Markov Process. Relat. Fields 16, No. 1, 169-184 (2010). Reviewer: Alexander Kachurovskij (Novosibirsk) MSC: 37A35 28D20 PDFBibTeX XMLCite \textit{A. M. Vershik}, Markov Process. Relat. Fields 16, No. 1, 169--184 (2010; Zbl 1203.37020) Full Text: arXiv
Vershik, A. M.; Gorbulsky, A. D. Scaled entropy of filtrations of \(\sigma\)-fields. (English. Russian original) Zbl 1161.28005 Theory Probab. Appl. 52, No. 3, 493-508 (2008); translation from Teor. Veroyatn. Primen. 52, No. 3, 446-467 (2007). Reviewer: Alexander Kachurovskij (Novosibirsk) MSC: 28D20 37A35 60G10 PDFBibTeX XMLCite \textit{A. M. Vershik} and \textit{A. D. Gorbulsky}, Theory Probab. Appl. 52, No. 3, 493--508 (2008; Zbl 1161.28005); translation from Teor. Veroyatn. Primen. 52, No. 3, 446--467 (2007) Full Text: DOI arXiv
Vershik, A. M. Does there exist a Lebesgue measure in the infinite-dimensional space? (English. Russian original) Zbl 1165.28003 Proc. Steklov Inst. Math. 259, 248-272 (2007); translation from Tr. Mat. Inst. Steklova 259, 256-281 (2007). Reviewer: Sergey Ludkovsky (Moskva) MSC: 28A33 28C20 46G12 PDFBibTeX XMLCite \textit{A. M. Vershik}, Proc. Steklov Inst. Math. 259, 248--272 (2007; Zbl 1165.28003); translation from Tr. Mat. Inst. Steklova 259, 256--281 (2007) Full Text: DOI arXiv
Vershik, A. M.; Haböck, U. Compactness of the congruence group of measurable functions in several variables. (English) Zbl 1127.28001 Zap. Nauchn. Semin. POMI 334, 57-67 (2006) and J. Math. Sci., New York 141, No. 6, 1601-1607 (2007). Reviewer: Hermann Render (Logrono) MSC: 28A20 46N99 PDFBibTeX XMLCite \textit{A. M. Vershik} and \textit{U. Haböck}, Zap. Nauchn. Semin. POMI 334, 57--67 (2006; Zbl 1127.28001) Full Text: Link
Vershik, A. M. The Kantorovich metric: the initial history and little-known applications. (English. Russian original) Zbl 1090.28009 J. Math. Sci., New York 133, No. 4, 1410-1417 (2006); translation from Zap. Nauchn. Semin. POMI 312, 69-85, 311 (2004). MSC: 28D05 01A60 49Q20 PDFBibTeX XMLCite \textit{A. M. Vershik}, J. Math. Sci., New York 133, No. 4, 1410--1417 (2006; Zbl 1090.28009); translation from Zap. Nauchn. Semin. POMI 312, 69--85, 311 (2004) Full Text: DOI EuDML
Vershik, A. M. Towards the definition of metric hyperbolicity. (English) Zbl 1109.37002 Mosc. Math. J. 5, No. 3, 721-737 (2005). MSC: 37A05 60J05 37A25 47A35 37A30 28D99 PDFBibTeX XMLCite \textit{A. M. Vershik}, Mosc. Math. J. 5, No. 3, 721--737 (2005; Zbl 1109.37002) Full Text: arXiv
Vershik, Anatoly M. Random and universal metric spaces. (English) Zbl 1124.28012 Maass, Alejandro (ed.) et al., Dynamics and randomness II. Lectures given at the 2nd conference, Santiago, Chile, December 9–13, 2002. Dordrecht: Kluwer Academic Publishers (ISBN 1-4020-1990-4/hbk). Nonlinear Phenomena and Complex Systems 10, 199-228 (2004). Reviewer: Su Gao (Denton) MSC: 28C15 PDFBibTeX XMLCite \textit{A. M. Vershik}, Nonlinear Phenom. Complex Syst. 10, 199--228 (2004; Zbl 1124.28012) Full Text: arXiv
Vershik, A. M. Kolmogorov’s example (A survey of actions of infinite-dimensional groups with an invariant probability measure). (English. Russian original) Zbl 1055.37006 Theory Probab. Appl. 48, No. 2, 373-378 (2003); translation from Teor. Veroyatn. Primen. 48, No. 2, 386-391 (2003). MSC: 37A15 28D15 37A40 37C40 PDFBibTeX XMLCite \textit{A. M. Vershik}, Theory Probab. Appl. 48, No. 2, 373--378 (2003; Zbl 1055.37006); translation from Teor. Veroyatn. Primen. 48, No. 2, 386--391 (2003) Full Text: DOI
Vershik, A. M.; Tsilevich, N. V. Fock factorizations and decompositions of the \(L^ 2\) spaces over general Lévy processes. (English. Russian original) Zbl 1060.46056 Russ. Math. Surv. 58, No. 3, 427-472 (2003); translation from Usp. Mat. Nauk 58, No. 3, 3-50 (2003). MSC: 46N30 28C20 46G99 60B15 60G51 60H40 81R10 PDFBibTeX XMLCite \textit{A. M. Vershik} and \textit{N. V. Tsilevich}, Russ. Math. Surv. 58, No. 3, 427--472 (2003; Zbl 1060.46056); translation from Usp. Mat. Nauk 58, No. 3, 3--50 (2003) Full Text: DOI arXiv
Vershik, A. M. Classification of measurable functions of several variables and invariantly distributed random matrices. (English. Russian original) Zbl 1025.28010 Funct. Anal. Appl. 36, No. 2, 93-105 (2002); translation from Funkts. Anal. Prilozh. 36, No. 2, 12-27 (2002). MSC: 28D05 60E05 28A35 15B52 37C40 PDFBibTeX XMLCite \textit{A. M. Vershik}, Funct. Anal. Appl. 36, No. 2, 93--105 (2002; Zbl 1025.28010); translation from Funkts. Anal. Prilozh. 36, No. 2, 12--27 (2002) Full Text: DOI
Vershik, A. M.; Yakubovich, Yu. V. Continuous lattices of partitions and lattices of continuous partitions. (English) Zbl 0997.06004 Uraltseva, N. N. (ed.), Proceedings of the St. Petersburg Mathematical Society. Vol. VII. Transl. from the Russian by Tamara Rozhkovskaya. Providence, RI: American Mathematical Society (AMS). Transl., Ser. 2, Am. Math. Soc. 203, 1-15 (2001). Reviewer: Jaromír Duda (Brno) MSC: 06B35 28B05 05A18 PDFBibTeX XMLCite \textit{A. M. Vershik} and \textit{Yu. V. Yakubovich}, Transl., Ser. 2, Am. Math. Soc. 203, 1--15 (2001; Zbl 0997.06004)
Tsilevich, Natalia; Vershik, Anatoly; Yor, Marc An infinite-dimensional analogue of the Lebesgue measure and distinguished properties of the gamma process. (English) Zbl 0990.60053 J. Funct. Anal. 185, No. 1, 274-296 (2001). Reviewer: V.Oganyan (Erevan) MSC: 60G51 60G52 28C20 PDFBibTeX XMLCite \textit{N. Tsilevich} et al., J. Funct. Anal. 185, No. 1, 274--296 (2001; Zbl 0990.60053) Full Text: DOI
Vershik, A. M. V. A. Rokhlin and the modern theory of measurable partitions. (English) Zbl 0977.01037 Turaev, V. (ed.) et al., Topology, ergodic theory, real algebraic geometry. Rokhlin’s memorial. Providence, RI: American Mathematical Society (AMS). Transl., Ser. 2, Am. Math. Soc. 202(50), 11-20 (2001). Reviewer: K.-B.Gundlach (Marburg) MSC: 01A70 01A60 28-03 PDFBibTeX XMLCite \textit{A. M. Vershik}, Transl., Ser. 2, Am. Math. Soc. 202, 11--20 (2001; Zbl 0977.01037)
Vershik, A. M. Numerical invariants of exponential groups and locally free approximation of the braid group. (English. Russian original) Zbl 1033.20500 J. Math. Sci., New York 113, No. 4, 569-575 (2003); translation from Zap. Nauchn. Semin. POMI 266, 51-63 (2000). MSC: 20F05 20F36 20F69 20E25 20E05 28D20 PDFBibTeX XMLCite \textit{A. M. Vershik}, J. Math. Sci., New York 113, No. 4, 569--575 (2000; Zbl 1033.20500); translation from Zap. Nauchn. Semin. POMI 266, 51--63 (2000) Full Text: DOI EuDML
Vershik, A. M. Numerical invariants of exponential groups and locally free approximation of the braid group. (Russian. English summary) Zbl 1023.20013 Zap. Nauchn. Semin. POMI 266, Pt. II, 51-63 (2000). Reviewer: E.S.Golod (Moskva) MSC: 20F05 20F36 20F69 20E25 20E05 28D20 PDFBibTeX XMLCite \textit{A. M. Vershik}, Zap. Nauchn. Semin. POMI 266, Part II, 51--63 (2000; Zbl 1023.20013) Full Text: EuDML
Vershik, A. M. Dynamic theory of growth in groups: Entropy, boundaries, examples. (English. Russian original) Zbl 0991.37005 Russ. Math. Surv. 55, No. 4, 667-733 (2000); translation from Usp. Mat. Nauk 55, No. 4, 59-128 (2000). Reviewer: Yasuhiro Asoo (Okayama) MSC: 37A35 28D20 PDFBibTeX XMLCite \textit{A. M. Vershik}, Russ. Math. Surv. 55, No. 4, 667--733 (2000; Zbl 0991.37005); translation from Usp. Mat. Nauk 55, No. 4, 59--128 (2000) Full Text: DOI
Vershik, A. M. Numerical characteristics of groups and the relations between them. (English. Russian original) Zbl 0996.20057 J. Math. Sci., New York 107, No. 5, 4147-4157 (2001); translation from Zap. Nauchn. Semin. POMI 256, 5-18 (1999). MSC: 20P05 20F05 60G50 20F69 28D20 60B15 PDFBibTeX XMLCite \textit{A. M. Vershik}, J. Math. Sci., New York 107, No. 5, 4147--4157 (1999; Zbl 0996.20057); translation from Zap. Nauchn. Semin. POMI 256, 5--18 (1999) Full Text: DOI
Sidorov, N.; Vershik, A. Bijective arithmetic codings of hyperbolic automorphisms of the \(2\)-torus, and binary quadratic forms. (English) Zbl 0949.37023 J. Dyn. Control Syst. 4, No. 3, 365-399 (1998). MSC: 37E35 11E16 28D05 PDFBibTeX XMLCite \textit{N. Sidorov} and \textit{A. Vershik}, J. Dyn. Control Syst. 4, No. 3, 365--399 (1998; Zbl 0949.37023) Full Text: DOI arXiv
Vershik, A. M.; Sidorov, N. A. Bijective coding of automorphisms of the torus and binary quadratic forms. (English. Russian original) Zbl 0934.37006 Russ. Math. Surv. 53, No. 5, 1106-1107 (1998); translation from Usp. Mat. Nauk. 53, No. 5, 231-232 (1998). Reviewer: Michael L.Blank (Moskva) MSC: 37A30 28D05 28D20 37A35 37B10 37D20 PDFBibTeX XMLCite \textit{A. M. Vershik} and \textit{N. A. Sidorov}, Russ. Math. Surv. 53, No. 5, 1106--1107 (1998; Zbl 0934.37006); translation from Usp. Mat. Nauk. 53, No. 5, 231--232 (1998) Full Text: DOI
Vershik, A. M. The universal Urysohn space, Gromov metric triples and random metrics on the natural numbers. (English. Russian original) Zbl 1005.53036 Russ. Math. Surv. 53, No. 5, 921-928 (1998); translation from Usp. Mat. Nauk. 53, No. 5, 57-64 (1998). MSC: 53C23 28D05 54E99 PDFBibTeX XMLCite \textit{A. M. Vershik}, Russ. Math. Surv. 53, No. 5, 921--928 (1998; Zbl 1005.53036); translation from Usp. Mat. Nauk. 53, No. 5, 57--64 (1998) Full Text: DOI
Sidorov, Nikita; Vershik, Anatoly Ergodic properties of the Erdős measure, the entropy of the goldenshift, and related problems. (English) Zbl 0916.28012 Monatsh. Math. 126, No. 3, 215-261 (1998). Reviewer: Thomas Ward (Norwich) MSC: 28D05 28D20 37E99 PDFBibTeX XMLCite \textit{N. Sidorov} and \textit{A. Vershik}, Monatsh. Math. 126, No. 3, 215--261 (1998; Zbl 0916.28012) Full Text: DOI arXiv EuDML
Ol’shanskij, Grigorij; Vershik, Anatolij Ergodic unitarily invariant measures on the space of infinite Hermitian matrices. (English) Zbl 0853.22016 Dobrushin, R. L. (ed.) et al., Contemporary mathematical physics. F. A. Berezin memorial volume. Transl. ed. by A. B. Sossinsky. Providence, RI: American Mathematical Society. Transl., Ser. 2, Am. Math. Soc. 175(31), 137-175 (1996). MSC: 22E65 28C10 PDFBibTeX XMLCite \textit{G. Ol'shanskij} and \textit{A. Vershik}, Transl., Ser. 2, Am. Math. Soc. 175, 137--175 (1996; Zbl 0853.22016) Full Text: arXiv
Vershik, A. M. The adic realizations of the ergodic actions with the homeomorphisms of the Markov compact and the ordered Bratteli diagrams. (English) Zbl 0884.28013 Vershik, A. M. (ed.), Representation theory, dynamical systems, combinatorial and algorithmic methods. I. Work collection. Sankt-Peterburg: Nauka. Zap. Nauchn. Semin. POMI. 223, 120-126 (1995). MSC: 28D05 28D15 46L55 PDFBibTeX XML
Vershik, A. M. Adic realizations of ergodic actions by homeomorphisms of Markov compacta and ordered Bratteli diagrams. (English. Russian original) Zbl 0909.28012 J. Math. Sci., New York 87, No. 6, 4054-4058 (1997); translation from Zap. Nauchn. Semin. POMI 223, 120-126 (1995). MSC: 28D05 28D15 46L55 PDFBibTeX XMLCite \textit{A. M. Vershik}, J. Math. Sci., New York 87, No. 6, 4054--4058 (1995; Zbl 0909.28012); translation from Zap. Nauchn. Semin. POMI 223, 120--126 (1995) Full Text: DOI
Vershik, A. M. The theory of decreasing sequences of measurable partitions. (English. Russian original) Zbl 0853.28009 St. Petersbg. Math. J. 6, No. 4, 705-761 (1995); translation from Algebra Anal. 6, No. 4, 1-68 (1994). Reviewer: V.Sharapov (Volgograd) MSC: 28D05 PDFBibTeX XMLCite \textit{A. M. Vershik}, St. Petersbg. Math. J. 6, No. 4, 1--68 (1994; Zbl 0853.28009); translation from Algebra Anal. 6, No. 4, 1--68 (1994)
Vershik, A. M. Locally transversal symbolic dynamics. (English. Russian original) Zbl 0839.58019 St. Petersbg. Math. J. 6, No. 3, 529-540 (1995); translation from Algebra Anal. 6, No. 3, 94-106 (1994). MSC: 37E99 37A99 28D05 PDFBibTeX XMLCite \textit{A. M. Vershik}, St. Petersbg. Math. J. 6, No. 3, 94--106 (1994; Zbl 0839.58019); translation from Algebra Anal. 6, No. 3, 94--106 (1994)
Vershik, A. M. Locally-transversal symbolic dynamics. (Russian) Zbl 0829.58012 Algebra Anal. 6, No. 3, 94-106 (1994). Reviewer: A.Klíč (Praha) MSC: 37E99 37A99 28D05 PDFBibTeX XMLCite \textit{A. M. Vershik}, Algebra Anal. 6, No. 3, 94--106 (1994; Zbl 0829.58012)
Vershik, A. M. Arithmetic isomorphism of hyperbolic toral automorphisms and sofic shifts. (English. Russian original) Zbl 0810.58031 Funct. Anal. Appl. 26, No. 3, 170-173 (1992); translation from Funkts. Anal. Prilozh. 26, No. 3, 22-27 (1992). Reviewer: Y.A.Brudnyi (Haifa) MSC: 37D99 28D05 PDFBibTeX XMLCite \textit{A. M. Vershik}, Funct. Anal. Appl. 26, No. 3, 170--173 (1992; Zbl 0810.58031); translation from Funkts. Anal. Prilozh. 26, No. 3, 22--27 (1992) Full Text: DOI
Vershik, A. M. (ed.) Representation theory and dynamical systems. Transl. ed. by A. B. Sossinsky. (English) Zbl 0745.00063 Advances in Soviet Mathematics. 9. Providence, RI: American Mathematical Society (AMS). viii, 267 p. (1992). MSC: 00B25 20-06 28-06 53-06 58-06 81-06 PDFBibTeX XMLCite \textit{A. M. Vershik} (ed.), Representation theory and dynamical systems. Transl. ed. by A. B. Sossinsky. Providence, RI: American Mathematical Society (1992; Zbl 0745.00063)
Vershik, A. M.; Livshits, A. N. Adic models of ergodic transformations, spectral theory, substitutions, and related topics. (English) Zbl 0770.28013 Representation theory and dynamical systems, Adv. Sov. Math. 9, 185-204 (1992). Reviewer: U.Krengel (Göttingen) MSC: 28D05 46L55 46L05 PDFBibTeX XMLCite \textit{A. M. Vershik} and \textit{A. N. Livshits}, Adv. Sov. Math. 9, 185--204 (1992; Zbl 0770.28013)
Vershik, A. M. On the work of V. A. Rokhlin in ergodic theory. (English. Russian original) Zbl 0721.01014 Leningr. Math. J. 2, No. 2, 427-431 (1991); translation from Algebra Anal. 2, No. 2, 236-241 (1990). MSC: 01A70 01A60 28-03 PDFBibTeX XMLCite \textit{A. M. Vershik}, Leningr. Math. J. 2, No. 2, 427--431 (1991; Zbl 0721.01014); translation from Algebra Anal. 2, No. 2, 236--241 (1990)
Vershik, A. M. On the papers of V. A. Rokhlin on ergodic theory. (Russian) Zbl 0706.01004 Algebra Anal. 2, No. 2, 236-241 (1990). Reviewer: D.Brânzei MSC: 01A60 28-03 PDFBibTeX XMLCite \textit{A. M. Vershik}, Algebra Anal. 2, No. 2, 236--241 (1990; Zbl 0706.01004)
Vershik, A. M. A new model of the ergodic transformations. (English) Zbl 0702.28006 Dynamical systems and ergodic theory, 28th Sem. St. Banach Int. Math. Cent., Warsaw/Pol. 1986, Banach Cent. Publ. 23, 381-384 (1989). Reviewer: V.V.Peller MSC: 28D05 28D10 PDFBibTeX XML
Martin, Nathaniel F. G.; England, James W. Vershik, A. M. (ed.) Mathematical theory of entropy. Transl. from the English by V. A. Kajmanovich. Transl. ed. and with a foreword by A. M. Vershik. (Matematicheskaya teoriya ehntropii.) (Russian) Zbl 0665.28012 Moskva: Mir. 352 p. R. 3.70 (1988). MSC: 28D20 37B40 54H20 60A05 82B05 94A17 94A24 28-01 PDFBibTeX XMLCite \textit{N. F. G. Martin} et al., Matematicheskaya teoriya ehntropii (Russian). Transl. from the English by V. A. Kajmanovich. Transl. ed. and with a foreword by A. M. Vershik. Moskva: Mir (1988; Zbl 0665.28012)
Vershik, A. M.; Fedorov, A. L. Trajectory theory. (English) Zbl 0628.28015 J. Sov. Math. 38, 1799-1822 (1987). MSC: 28D99 PDFBibTeX XMLCite \textit{A. M. Vershik} and \textit{A. L. Fedorov}, J. Sov. Math. 38, 1799--1822 (1987; Zbl 0628.28015) Full Text: DOI
Vershik, A. M. Measurable realizations of groups of automorphisms, and integral representations of positive operators. (English. Russian original) Zbl 0627.47012 Sib. Math. J. 28, No. 1-2, 36-43 (1987); translation from Sib. Mat. Zh. 28, No. 1(161), 52-60 (1987). Reviewer: F.-H.Vasilescu MSC: 47B38 47B60 47D03 28D99 47A35 PDFBibTeX XMLCite \textit{A. M. Vershik}, Sib. Math. J. 28, No. 1--2, 36--43 (1987; Zbl 0627.47012); translation from Sib. Mat. Zh. 28, No. 1(161), 52--60 (1987) Full Text: DOI
Kornfel’d, I. P.; Sinai, Ya. G.; Vershik, A. M. General ergodic theory of groups of measure preserving transformations. (English. Russian original) Zbl 0781.58016 Dynamical systems. II. Ergodic theory with applications to dynamical systems and statistical mechanics. Encycl. Math. Sci. 2, 1-98 (1989); translation from Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat., Fundam. Napravleniya 2, 5-111 (1985). MSC: 37A25 37A30 28D05 37A05 PDFBibTeX XMLCite \textit{I. P. Kornfel'd} et al., Encycl. Math. Sci. 2, 1 (1985; Zbl 0781.58016); translation from Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat., Fundam. Napravleniya 2, 5--111 (1985)
Vershik, A. M.; Fedorov, A. L. Trajectory theory. (Russian) Zbl 0614.28018 Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat. 26, 171-211 (1985). Reviewer: W.Jarczyk MSC: 28D99 PDFBibTeX XML
Lodkin, A. A.; Vershik, A. M. Approximation for actions of amenable groups and transversal automorphisms. (English) Zbl 0584.28008 Operator algebras and their connections with topology and ergodic theory, Proc. Conf., Buşteni/Rom. 1983, Lect. Notes Math. 1132, 331-346 (1985). MSC: 28D15 47A35 46L55 PDFBibTeX XML
Vershik, A. M. A theorem on the Markov periodic approximation in ergodic theory. (English) Zbl 0559.47006 J. Sov. Math. 28, 667-674 (1985). MSC: 47A35 28D05 PDFBibTeX XMLCite \textit{A. M. Vershik}, J. Sov. Math. 28, 667--674 (1985; Zbl 0559.47006) Full Text: DOI
Kaimanovich, V. A.; Vershik, A. M. Random walks on discrete groups: Boundary and entropy. (English) Zbl 0641.60009 Ann. Probab. 11, 457-490 (1983). MSC: 60B15 22D40 28D20 43A07 20F99 60G50 60J50 PDFBibTeX XMLCite \textit{V. A. Kaimanovich} and \textit{A. M. Vershik}, Ann. Probab. 11, 457--490 (1983; Zbl 0641.60009) Full Text: DOI
Vershik, A. M. Many-valued measure-preserving mappings (polymorphisms) and Markovian operators. (English) Zbl 0517.28016 J. Sov. Math. 23, 2243-2266 (1983). MSC: 28D05 47A35 47A20 47D03 60J05 PDFBibTeX XMLCite \textit{A. M. Vershik}, J. Sov. Math. 23, 2243--2266 (1983; Zbl 0517.28016) Full Text: DOI
Vershik, A. M. A theorem on periodical Markov approximation in ergodic theory. (English) Zbl 0517.47005 Ergodic theory and related topics, Proc. Conf., Vitte/Hiddensee (GDR) 1981, Math. Res. 12, 195-206 (1982). MSC: 47A35 28D05 46L05 PDFBibTeX XML
Vershik, A. M. The theorem about the periodic Markov approximation in ergodic theory. (Russian) Zbl 0505.47006 Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 115, 72-82 (1982). MSC: 47A35 28D05 PDFBibTeX XMLCite \textit{A. M. Vershik}, Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 115, 72--82 (1982; Zbl 0505.47006) Full Text: EuDML
Vershik, A. M.; Kajmanovich, V. A. Random walks on groups: Boundary, entropy, uniform distribution. (English. Russian original) Zbl 0442.60069 Sov. Math., Dokl. 20, 1170-1173 (1979); translation from Dokl. Akad. Nauk SSSR 249, 15-18 (1979). MSC: 60G50 60J50 60B15 20P05 28C10 PDFBibTeX XMLCite \textit{A. M. Vershik} and \textit{V. A. Kajmanovich}, Sov. Math., Dokl. 20, 1170--1173 (1979; Zbl 0442.60069); translation from Dokl. Akad. Nauk SSSR 249, 15--18 (1979)
Birman, M. Sh.; Vershik, A. M.; Solomyak, M. Z. Product of commuting spectral measures need not be countably additive. (English) Zbl 0423.28008 Funct. Anal. Appl. 13, 48-49 (1979). MSC: 28B05 46G10 47A60 47A70 PDFBibTeX XMLCite \textit{M. Sh. Birman} et al., Funct. Anal. Appl. 13, 48--49 (1979; Zbl 0423.28008) Full Text: DOI
Birman, M. S.; Vershik, A. M.; Solomyak, M. Z. Das Produkt permutierbarer Spektralmaße kann nicht abzählbaradditiv sein. (Russian) Zbl 0406.28011 Funkts. Anal. Prilozh. 13, No. 1, 61-62 (1979). MSC: 28B05 46G10 PDFBibTeX XMLCite \textit{M. S. Birman} et al., Funkts. Anal. Prilozh. 13, No. 1, 61--62 (1979; Zbl 0406.28011)
Vershik, A. M. The action of \(\text{PSL}(2,\mathbb{Z})\) on \(\mathbb{R}^1\) is approximable. (English) Zbl 0399.28008 Russ. Math. Surv. 33, No. 1, 221-222 (1978); translation from Usp. Mat. Nauk 33, No. 1(199), 209-210 (1978). MSC: 28C10 28D15 PDFBibTeX XMLCite \textit{A. M. Vershik}, Russ. Math. Surv. 33, No. 1, 221--222 (1978; Zbl 0399.28008); translation from Usp. Mat. Nauk 33, No. 1(199), 209--210 (1978) Full Text: DOI
Vershik, A. M. The action of \(\text{PSL}(2,\mathbb Z)\) on \(\mathbb R^1\) is approximable. (Russian) Zbl 0391.28008 Usp. Mat. Nauk 33, No. 1(199), 209-210 (1978). MSC: 28C10 28D15 22F10 37A15 PDFBibTeX XMLCite \textit{A. M. Vershik}, Usp. Mat. Nauk 33, No. 1(199), 209--210 (1978; Zbl 0391.28008)
Vershik, A. M. Multivalued mappings with invariant measure (polymorphisms) and Markov operators. (Russian) Zbl 0408.28014 Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 72, 26-61 (1977). MSC: 28D05 60J05 47A35 47A20 47D03 PDFBibTeX XMLCite \textit{A. M. Vershik}, Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 72, 26--61 (1977; Zbl 0408.28014) Full Text: EuDML
Vershik, A. M. On D. Ornstein’s papers, weak dependence conditions and classes of stationary measures. (English. Russian original) Zbl 0364.60057 Theory Probab. Appl. 21(1976), 655-657 (1977); translation from Teor. Veroyatn. Primen. 21, 673-675 (1976). MSC: 60G05 60B10 28D05 PDFBibTeX XMLCite \textit{A. M. Vershik}, Theory Probab. Appl. 21, 655--657 (1976; Zbl 0364.60057); translation from Teor. Veroyatn. Primen. 21, 673--675 (1976)
Vershik, A. M.; Ladyzhenskaya, O. A. On the evolution of measures defined by the Navier-Stokes equations, and on the solvability of the Cauchy problem for Hopf’s statistical equation. (English. Russian original) Zbl 0338.35074 Sov. Math., Dokl. 17, 18-22 (1976); translation from Dokl. Akad. Nauk SSSR 226, 26-29 (1976). MSC: 35Q30 76D05 28D05 PDFBibTeX XMLCite \textit{A. M. Vershik} and \textit{O. A. Ladyzhenskaya}, Sov. Math., Dokl. 17, 18--22 (1976; Zbl 0338.35074); translation from Dokl. Akad. Nauk SSSR 226, 26--29 (1976)
Vershik, A. M. Description of invariant measures for the actions of some infinite- dimensional groups. (English. Russian original) Zbl 0324.28014 Sov. Math., Dokl. 15, 1396-1400 (1974); translation from Dokl. Akad. Nauk SSSR 218, 749-752 (1974). MSC: 28D05 28C10 54A20 37A05 PDFBibTeX XMLCite \textit{A. M. Vershik}, Sov. Math., Dokl. 15, 1396--1400 (1974; Zbl 0324.28014); translation from Dokl. Akad. Nauk SSSR 218, 749--752 (1974)
Vershik, A. M. Four definitions of the scale of an automorphism. (English. Russian original) Zbl 0299.28016 Funct. Anal. Appl. 7, 169-181 (1974); translation from Funkts. Anal. Prilozh. 7, No. 3, 1-17 (1973). MSC: 28D05 PDFBibTeX XMLCite \textit{A. M. Vershik}, Funct. Anal. Appl. 7, 169--181 (1974; Zbl 0299.28016); translation from Funkts. Anal. Prilozh. 7, No. 3, 1--17 (1973) Full Text: DOI
Vershik, A. M.; Gel’fand, I. M.; Graev, M. I. Representations of the group \(\text{SL}(2, R)\), where \(R\) is a ring of functions. (English) Zbl 0297.22003 Russ. Math. Surv. 28, No. 5, 87-132 (1973); translation from Usp. Mat. Nauk 28, No. 5(173), 82-128 (1973). MSC: 22A15 22E15 54C35 22D10 28C20 PDFBibTeX XMLCite \textit{A. M. Vershik} et al., Russ. Math. Surv. 28, No. 5, 87--132 (1973; Zbl 0297.22003); translation from Usp. Mat. Nauk 28, No. 5(173), 82--128 (1973) Full Text: DOI
Vershik, A. M. A metric invariant of automorphisms of a measure space connected with uniform approximation and sequences of partitions. (English. Russian original) Zbl 0289.28014 Sov. Math., Dokl. 14, 297-301 (1973); translation from Dokl. Akad. Nauk SSSR 209, 15-18 (1973). MSC: 28D05 54H15 37A05 PDFBibTeX XMLCite \textit{A. M. Vershik}, Sov. Math., Dokl. 14, 297--301 (1973; Zbl 0289.28014); translation from Dokl. Akad. Nauk SSSR 209, 15--18 (1973)
Vershik, A. M.; Gel’fand, I. M.; Graev, M. I. Representations of the group \(\text{SL}(2, R)\), where \(R\) is a ring of functions. (Russian) Zbl 0288.22005 Usp. Mat. Nauk 28, No. 5(173), 82-128 (1973). Reviewer: K. Strambach MSC: 22A15 22E15 54C35 22D10 28C20 PDFBibTeX XMLCite \textit{A. M. Vershik} et al., Usp. Mat. Nauk 28, No. 5(173), 82--128 (1973; Zbl 0288.22005)
Vershik, A. M. A device for tame partitions. (Russian) Zbl 0248.28012 Usp. Mat. Nauk 27, No. 3(165), 195-196 (1972). MSC: 28D05 PDFBibTeX XMLCite \textit{A. M. Vershik}, Usp. Mat. Nauk 27, No. 3(165), 195--196 (1972; Zbl 0248.28012)
Vershik, A. M. Continuum of pairwise nonisomorphic dyadic sequences. (English. Russian original) Zbl 0244.28009 Funct. Anal. Appl. 5, 182-184 (1972); translation from Funkts. Anal. Prilozh. 5, No. 3, 16-18 (1971). MSC: 28D05 60J99 PDFBibTeX XMLCite \textit{A. M. Vershik}, Funct. Anal. Appl. 5, 182--184 (1972; Zbl 0244.28009); translation from Funkts. Anal. Prilozh. 5, No. 3, 16--18 (1971) Full Text: DOI
Vershik, A. M. Nonmeasurable decompositions, orbit theory, algebras of operators. (English. Russian original) Zbl 0228.28013 Sov. Math., Dokl. 12, 1218-1222 (1971); translation from Dokl. Akad. Nauk SSSR 199, 1004-1007 (1971). MSC: 28D10 28D05 PDFBibTeX XMLCite \textit{A. M. Vershik}, Sov. Math., Dokl. 12, 1218--1222 (1971; Zbl 0228.28013); translation from Dokl. Akad. Nauk SSSR 199, 1004--1007 (1971)
Vershik, A. M.; Yuzvinskii, S. A. Dynamical systems with invariant measure. (English) Zbl 0252.28006 Progress Math. 8, 151-215 (1970). MSC: 28D05 54H20 47A35 37-XX PDFBibTeX XML
Vershik, A. M. Decreasing sequences of measurable partitions and their applications. (English. Russian original) Zbl 0238.28011 Sov. Math., Dokl. 11, 1007-1011 (1970); translation from Dokl. Akad. Nauk SSSR 193, 748-751 (1970). MSC: 28D05 PDFBibTeX XMLCite \textit{A. M. Vershik}, Sov. Math., Dokl. 11, 1007--1011 (1970; Zbl 0238.28011); translation from Dokl. Akad. Nauk SSSR 193, 748--751 (1970)
Vershik, A. M.; Sudakov, V. N. Probability measures in infinite-dimensional spaces. (English. Russian original) Zbl 0248.60007 Semin. Math., V. A. Steklov Math. Inst., Leningrad 12, 1-28 (1969); translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklov 12, 7-67 (1969). MSC: 60B05 28C20 PDFBibTeX XML