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Author ID: spitzer.frank-l Recent zbMATH articles by "Spitzer, Frank L."
Published as: Spitzer, Frank; Spitzer, F.; Spitzer, Frank L.; Spitzer, F. L.
External Links: MGP · Wikidata · Math-Net.Ru · GND · IdRef
Documents Indexed: 50 Publications since 1955, including 7 Books
Biographic References: 1 Publication
Co-Authors: 14 Co-Authors with 17 Joint Publications
379 Co-Co-Authors

Publications by Year

Citations contained in zbMATH Open

46 Publications have been cited 2,277 times in 2,071 Documents Cited by Year
Principles of random walk. Zbl 0119.34304
Spitzer, F.
393
1964
Interaction of Markov processes. Zbl 0312.60060
Spitzer, Frank
267
1970
Principles of random walk. 2nd ed. Zbl 0359.60003
Spitzer, Frank
238
1976
A combinatorial lemma and its application to probability theory. Zbl 0071.13003
Spitzer, Frank
235
1956
A limit law for random walk in a random environment. Zbl 0388.60069
Kesten, H.; Kozlov, M. V.; Spitzer, F.
167
1975
Some theorems concerning 2-dimensional Brownian motion. Zbl 0089.13601
Spitzer, Frank
112
1958
A limit theorem related to a new class of self similar processes. Zbl 0396.60037
Kesten, H.; Spitzer, F.
105
1979
Markov random fields on an infinite tree. Zbl 0313.60072
Spitzer, Frank
81
1975
Electrostatic capacity, heat-flow, and Brownian motion. Zbl 0126.33505
Spitzer, F.
69
1964
Principles of random walk. 2nd ed. 1976, 2nd print. Zbl 0979.60002
Spitzer, Frank
59
2001
The Toeplitz matrices of an arbitrary Laurent polynomial. Zbl 0101.09203
Schmidt, Palle; Spitzer, Frank
50
1960
Ergodic theorems for coupled random walks and other systems with locally interacting components. Zbl 0444.60096
Liggett, Thomas M.; Spitzer, Frank
41
1981
The Wiener-Hopf equation whose kernel is a probability density. Zbl 0082.32003
Spitzer, Frank
39
1957
The Galton-Watson process with mean one and finite variance. Zbl 0158.35202
Kesten, H.; Ney, P.; Spitzer, F.
37
1966
Markov random fields and Gibbs ensembles. Zbl 0241.60094
Spitzer, Frank
35
1971
Convergence in distribution of products of random matrices. Zbl 0535.60016
Kesten, Harry; Spitzer, Frank
35
1984
On multitype branching processes with \(\rho\leq1\). Zbl 0178.19504
Joffe, A.; Spitzer, F.
34
1967
The Martin boundary for random walk. Zbl 0141.15601
Ney, P.; Spitzer, F.
33
1966
A Tauberian theorem and its probability interpretation. Zbl 0216.21201
Spitzer, F.
31
1960
Inversion of Toeplitz matrices. Zbl 0091.11101
Calderón, Alberto P.; Spitzer, Frank; Widom, Harold
27
1959
Interacting particle systems at Saint-Flour. Reprint of lectures originally published in the Lecture Notes in Mathematics volumes 1608 (1995), 1464 (1991), 589 (1977), and 390 (1974). Zbl 1248.82021
Durrett, Rick; Liggett, Thomas M.; Spitzer, Frank; Sznitman, Alain-Sol
18
2012
Stochastic time evolution of one dimensional infinite particle systems. Zbl 0372.60149
Spitzer, Frank
16
1977
Ratio theorems for random walks. I. Zbl 0121.35201
Kesten, H.; Spitzer, F.
16
1963
The circumference of a convex polygon. Zbl 0099.38501
Spitzer, F.; Widom, H.
15
1961
A class of Toeplitz forms and their application to probability theory. Zbl 0124.34403
Spitzer, F. L.; Stone, C. J.
14
1960
Recurrent random walk of an infinite particle system. Zbl 0321.60087
Spitzer, Frank
13
1974
Random walk on countably infinite Abelian groups. Zbl 0146.38301
Kesten, H.; Spitzer, F.
13
1965
Random processes defined through the interaction of an infinite particle system. Zbl 0181.43601
Spitzer, F.
11
1969
A variational characterization of finite Markov chains. Zbl 0238.60093
Spitzer, Frank
10
1972
Phase transition in one-dimensional nearest-neighbor systems. Zbl 0333.60063
Spitzer, Frank
9
1975
The Wiener-Hopf equation whose kernel is a probability density. II. Zbl 0111.30101
Spitzer, F.
9
1960
Hitting probabilities. Zbl 0218.60061
Spitzer, F.
8
1962
Infinite systems with locally interacting components. Zbl 0462.60096
Spitzer, Frank
7
1981
Principles of random walk. Übersetzung aus dem Englischen von O.V.Viskov u. E.V. Chepurin Redaktion von Eh.L. Presman und Y.V.Prokhorov. Zbl 0175.16702
Spitzer, F.
6
1969
Some properties of recurrent random walk. Zbl 0109.36201
Spitzer, F.
5
1961
Recurrent random walk and logarithmic potential. Zbl 0107.35505
Spitzer, F.
4
1961
A multidimensional renewal theorem. Zbl 0608.60083
Spitzer, Frank
4
1986
Controlled Markov chains. Zbl 0318.60070
Kesten, Harry; Spitzer, Frank
2
1975
A general property of random walk. Zbl 0111.32701
Kesten, H.; Ornstein, D.; Spitzer, F.
2
1962
Renewal theorems for Markov chains. Zbl 0219.60073
Spitzer, F.
1
1967
Ecole d’ete de probabilites de Saint-Flour III - 1973. Edite par A. Badrikian et P.-L. Hennequin. Zbl 0277.00014
Meyer, P. A.; Priouret, P.; Spitzer, F.
1
1974
Introduction aux processus de Markov à paramètre dans \(\mathbb{Z}_\nu\). Zbl 0343.60042
Spitzer, Frank L.
1
1974
The characterization of optimal saving programs in a quadratic model. Zbl 0346.90012
Spitzer, Frank; Wan, Henry jun.
1
1976
On a class of random variables. Zbl 0064.12803
Spitzer, Frank
1
1955
Two explicit Martin boundary constructions. Zbl 0158.12802
Spitzer, F.
1
1967
Random time evolution of infinite particle systems. Zbl 0361.60087
Spitzer, Frank
1
1975
Interacting particle systems at Saint-Flour. Reprint of lectures originally published in the Lecture Notes in Mathematics volumes 1608 (1995), 1464 (1991), 589 (1977), and 390 (1974). Zbl 1248.82021
Durrett, Rick; Liggett, Thomas M.; Spitzer, Frank; Sznitman, Alain-Sol
18
2012
Principles of random walk. 2nd ed. 1976, 2nd print. Zbl 0979.60002
Spitzer, Frank
59
2001
A multidimensional renewal theorem. Zbl 0608.60083
Spitzer, Frank
4
1986
Convergence in distribution of products of random matrices. Zbl 0535.60016
Kesten, Harry; Spitzer, Frank
35
1984
Ergodic theorems for coupled random walks and other systems with locally interacting components. Zbl 0444.60096
Liggett, Thomas M.; Spitzer, Frank
41
1981
Infinite systems with locally interacting components. Zbl 0462.60096
Spitzer, Frank
7
1981
A limit theorem related to a new class of self similar processes. Zbl 0396.60037
Kesten, H.; Spitzer, F.
105
1979
Stochastic time evolution of one dimensional infinite particle systems. Zbl 0372.60149
Spitzer, Frank
16
1977
Principles of random walk. 2nd ed. Zbl 0359.60003
Spitzer, Frank
238
1976
The characterization of optimal saving programs in a quadratic model. Zbl 0346.90012
Spitzer, Frank; Wan, Henry jun.
1
1976
A limit law for random walk in a random environment. Zbl 0388.60069
Kesten, H.; Kozlov, M. V.; Spitzer, F.
167
1975
Markov random fields on an infinite tree. Zbl 0313.60072
Spitzer, Frank
81
1975
Phase transition in one-dimensional nearest-neighbor systems. Zbl 0333.60063
Spitzer, Frank
9
1975
Controlled Markov chains. Zbl 0318.60070
Kesten, Harry; Spitzer, Frank
2
1975
Random time evolution of infinite particle systems. Zbl 0361.60087
Spitzer, Frank
1
1975
Recurrent random walk of an infinite particle system. Zbl 0321.60087
Spitzer, Frank
13
1974
Ecole d’ete de probabilites de Saint-Flour III - 1973. Edite par A. Badrikian et P.-L. Hennequin. Zbl 0277.00014
Meyer, P. A.; Priouret, P.; Spitzer, F.
1
1974
Introduction aux processus de Markov à paramètre dans \(\mathbb{Z}_\nu\). Zbl 0343.60042
Spitzer, Frank L.
1
1974
A variational characterization of finite Markov chains. Zbl 0238.60093
Spitzer, Frank
10
1972
Markov random fields and Gibbs ensembles. Zbl 0241.60094
Spitzer, Frank
35
1971
Interaction of Markov processes. Zbl 0312.60060
Spitzer, Frank
267
1970
Random processes defined through the interaction of an infinite particle system. Zbl 0181.43601
Spitzer, F.
11
1969
Principles of random walk. Übersetzung aus dem Englischen von O.V.Viskov u. E.V. Chepurin Redaktion von Eh.L. Presman und Y.V.Prokhorov. Zbl 0175.16702
Spitzer, F.
6
1969
On multitype branching processes with \(\rho\leq1\). Zbl 0178.19504
Joffe, A.; Spitzer, F.
34
1967
Renewal theorems for Markov chains. Zbl 0219.60073
Spitzer, F.
1
1967
Two explicit Martin boundary constructions. Zbl 0158.12802
Spitzer, F.
1
1967
The Galton-Watson process with mean one and finite variance. Zbl 0158.35202
Kesten, H.; Ney, P.; Spitzer, F.
37
1966
The Martin boundary for random walk. Zbl 0141.15601
Ney, P.; Spitzer, F.
33
1966
Random walk on countably infinite Abelian groups. Zbl 0146.38301
Kesten, H.; Spitzer, F.
13
1965
Principles of random walk. Zbl 0119.34304
Spitzer, F.
393
1964
Electrostatic capacity, heat-flow, and Brownian motion. Zbl 0126.33505
Spitzer, F.
69
1964
Ratio theorems for random walks. I. Zbl 0121.35201
Kesten, H.; Spitzer, F.
16
1963
Hitting probabilities. Zbl 0218.60061
Spitzer, F.
8
1962
A general property of random walk. Zbl 0111.32701
Kesten, H.; Ornstein, D.; Spitzer, F.
2
1962
The circumference of a convex polygon. Zbl 0099.38501
Spitzer, F.; Widom, H.
15
1961
Some properties of recurrent random walk. Zbl 0109.36201
Spitzer, F.
5
1961
Recurrent random walk and logarithmic potential. Zbl 0107.35505
Spitzer, F.
4
1961
The Toeplitz matrices of an arbitrary Laurent polynomial. Zbl 0101.09203
Schmidt, Palle; Spitzer, Frank
50
1960
A Tauberian theorem and its probability interpretation. Zbl 0216.21201
Spitzer, F.
31
1960
A class of Toeplitz forms and their application to probability theory. Zbl 0124.34403
Spitzer, F. L.; Stone, C. J.
14
1960
The Wiener-Hopf equation whose kernel is a probability density. II. Zbl 0111.30101
Spitzer, F.
9
1960
Inversion of Toeplitz matrices. Zbl 0091.11101
Calderón, Alberto P.; Spitzer, Frank; Widom, Harold
27
1959
Some theorems concerning 2-dimensional Brownian motion. Zbl 0089.13601
Spitzer, Frank
112
1958
The Wiener-Hopf equation whose kernel is a probability density. Zbl 0082.32003
Spitzer, Frank
39
1957
A combinatorial lemma and its application to probability theory. Zbl 0071.13003
Spitzer, Frank
235
1956
On a class of random variables. Zbl 0064.12803
Spitzer, Frank
1
1955
all top 5

Cited by 2,060 Authors

25 den Hollander, Frank
21 Csáki, Endre
18 Uchiyama, Kôhei
17 van den Berg, Michiel
16 Peres, Yuval
16 Révész, Pál
16 Spitzer, Frank L.
15 Liggett, Thomas Milton
15 Rozikov, Utkir A.
13 Földes, Antónia
13 Shi, Zhan
13 Yor, Marc
12 Greven, Andreas
12 Guillotin-Plantard, Nadine
12 Kesten, Harry
12 Mukhamedov, Farruh Maksutovich
12 Vatutin, Vladimir Alekseevich
11 Böttcher, Albrecht
11 Ferrari, Pablo Augusto
11 Gantert, Nina
11 Le Gall, Jean-François
11 Petrov, Leonid
11 Seppäläinen, Timo
10 Borodin, Alexei
10 Buraczewski, Dariusz
10 Cox, J. Theodore
10 Dolgopyat, Dmitry
10 Doney, Ronald Arthur
10 Großkinsky, Stefan
10 Gut, Allan
10 Khoshnevisan, Davar
10 Pène, Françoise
10 Peterson, Jonathon
10 Sznitman, Alain-Sol
10 Widom, Harold
9 Afanas’ev, Valeriĭ Ivanovich
9 D’yakonova, Elena Evgen’evna
9 Jain, Naresh C.
9 Majumdar, Satya N.
9 Maller, Ross Arthur
9 Mountford, Thomas S.
9 Redig, Frank
9 Spătaru, Aurel
9 Zeitouni, Ofer
8 Andjel, Enrique Daniel
8 Corwin, Ivan Z.
8 Deuschel, Jean-Dominique
8 Durrett, Richard Timothy
8 Ebrahimi-Fard, Kurusch
8 Fribergh, Alexander
8 Goldsheid, Ilya Ya.
8 Hu, Yueyun
8 Schütz, Gunter M.
8 Song, Renming
8 Wade, Andrew R.
7 Balazs, Marton
7 Baxter, Glen Earl
7 Benjamini, Itai
7 Bolthausen, Erwin
7 Corteel, Sylvie
7 Gonçalves, Patrícia C.
7 Grudsky, Sergei Mikhailovich
7 Hamana, Yuji
7 Haydarov, Farhod Halimjonovich
7 Lawler, Gregory Francis
7 Lebowitz, Joel Louis
7 Port, Sidney Charles
7 Vysotsky, Vladislav V.
7 Williams, Lauren K.
6 Bendikov, Alexander D.
6 Comets, Francis M.
6 Csörgő, Miklós
6 Dawson, Donald Andrew
6 Eshkabilov, Yusup Khalbaevich
6 Fleischmann, Klaus
6 Godrèche, Claude
6 Guivarc’h, Yves
6 Jara, Milton D.
6 Le Jan, Yves
6 Perkins, Edwin A.
6 Rassoul-Agha, Firas
6 Sandrić, Nikola
6 Souissi, Abdessatar
6 Tracy, Craig Arnold
6 van Leeuwaarden, Johan S. H.
6 Wang, Xuejun
6 Weiss, Neil A.
6 Zang, Qingpei
5 Accardi, Luigi
5 Albeverio, Sergio A.
5 Avena, Luca
5 Bass, Richard F.
5 Ben Arous, Gérard
5 Castell, Fabienne
5 Chen, Xia
5 Chleboun, Paul
5 Cocozza-Thivent, Christiane
5 Comtet, Alain
5 Cygan, Wojciech
5 Dembo, Amir
...and 1,960 more Authors
all top 5

Cited in 340 Serials

153 Stochastic Processes and their Applications
122 Probability Theory and Related Fields
117 Journal of Statistical Physics
115 The Annals of Probability
104 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
61 Journal of Theoretical Probability
58 Statistics & Probability Letters
57 Transactions of the American Mathematical Society
51 Communications in Mathematical Physics
41 Journal of Mathematical Analysis and Applications
41 Electronic Journal of Probability
36 The Annals of Applied Probability
34 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques
27 Journal of Statistical Mechanics: Theory and Experiment
22 Proceedings of the American Mathematical Society
21 Potential Analysis
18 Advances in Applied Probability
18 Journal of Functional Analysis
17 Journal d’Analyse Mathématique
16 Electronic Communications in Probability
15 Advances in Mathematics
15 Journal of Soviet Mathematics
13 Annales de l’Institut Fourier
13 Journal of Applied Probability
12 Israel Journal of Mathematics
12 Annales de l’Institut Henri Poincaré. Nouvelle Série. Section B. Calcul des Probabilités et Statistique
12 Mathematical Physics, Analysis and Geometry
12 ALEA. Latin American Journal of Probability and Mathematical Statistics
11 Linear Algebra and its Applications
11 Bulletin of the American Mathematical Society
10 Theoretical and Mathematical Physics
10 Journal of Multivariate Analysis
10 Bernoulli
10 Acta Mathematica Sinica. English Series
10 Journal of the Australian Mathematical Society
10 Journal of Physics A: Mathematical and Theoretical
9 Lithuanian Mathematical Journal
9 Ukrainian Mathematical Journal
9 Communications in Statistics. Theory and Methods
9 Comptes Rendus. Mathématique. Académie des Sciences, Paris
8 Journal of Mathematical Physics
8 Mathematical Notes
8 Siberian Mathematical Journal
8 Advances in Applied Mathematics
8 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics
7 Journal of Mathematical Biology
7 Mathematical Biosciences
7 Physica A
7 Integral Equations and Operator Theory
7 Acta Applicandae Mathematicae
7 Frontiers of Mathematics in China
6 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série
6 Compositio Mathematica
6 Duke Mathematical Journal
6 Inventiones Mathematicae
6 Monatshefte für Mathematik
6 Theoretical Computer Science
6 Insurance Mathematics & Economics
6 Stochastic Analysis and Applications
6 Acta Mathematica Hungarica
6 Queueing Systems
6 Journal of Mathematical Sciences (New York)
6 Proceedings of the Steklov Institute of Mathematics
6 Probability Surveys
5 Communications on Pure and Applied Mathematics
5 Letters in Mathematical Physics
5 Periodica Mathematica Hungarica
5 Theory of Probability and its Applications
5 Acta Mathematica
5 Journal of Combinatorial Theory. Series A
5 Journal of Statistical Planning and Inference
5 Theoretical Population Biology
5 Random Structures & Algorithms
5 Discrete Mathematics and Applications
5 The Electronic Journal of Combinatorics
5 Journal of Inequalities and Applications
5 Quantum Information Processing
5 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
5 Science China. Mathematics
4 Computers & Mathematics with Applications
4 Mathematical Proceedings of the Cambridge Philosophical Society
4 Nonlinearity
4 Arkiv för Matematik
4 Annales Scientifiques de l’Université de Clermont-Ferrand II. Mathématiques
4 Journal of Approximation Theory
4 Journal of Computational and Applied Mathematics
4 Mathematische Nachrichten
4 Mathematische Zeitschrift
4 Ergodic Theory and Dynamical Systems
4 Journal of Time Series Analysis
4 Bulletin of the American Mathematical Society. New Series
4 Acta Mathematica Sinica. New Series
4 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
4 Mathematical Methods of Statistics
4 Combinatorics, Probability and Computing
4 Extremes
4 Journal of the European Mathematical Society (JEMS)
4 Stochastics and Dynamics
4 Annales Henri Lebesgue
3 Acta Mathematica Academiae Scientiarum Hungaricae
...and 240 more Serials
all top 5

Cited in 55 Fields

1,579 Probability theory and stochastic processes (60-XX)
451 Statistical mechanics, structure of matter (82-XX)
125 Combinatorics (05-XX)
95 Statistics (62-XX)
74 Partial differential equations (35-XX)
69 Dynamical systems and ergodic theory (37-XX)
64 Operator theory (47-XX)
58 Linear and multilinear algebra; matrix theory (15-XX)
56 Biology and other natural sciences (92-XX)
48 Numerical analysis (65-XX)
45 Computer science (68-XX)
41 Quantum theory (81-XX)
40 Measure and integration (28-XX)
40 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
39 Potential theory (31-XX)
33 Operations research, mathematical programming (90-XX)
26 Functional analysis (46-XX)
18 Group theory and generalizations (20-XX)
17 Number theory (11-XX)
17 Functions of a complex variable (30-XX)
17 Integral equations (45-XX)
16 Harmonic analysis on Euclidean spaces (42-XX)
15 Special functions (33-XX)
14 Approximations and expansions (41-XX)
14 Abstract harmonic analysis (43-XX)
14 Global analysis, analysis on manifolds (58-XX)
13 Systems theory; control (93-XX)
11 Associative rings and algebras (16-XX)
11 Nonassociative rings and algebras (17-XX)
10 Topological groups, Lie groups (22-XX)
10 Convex and discrete geometry (52-XX)
10 Information and communication theory, circuits (94-XX)
9 Fluid mechanics (76-XX)
8 Ordinary differential equations (34-XX)
7 Real functions (26-XX)
6 Mathematical logic and foundations (03-XX)
6 Integral transforms, operational calculus (44-XX)
5 Mechanics of particles and systems (70-XX)
5 Classical thermodynamics, heat transfer (80-XX)
4 History and biography (01-XX)
4 Difference and functional equations (39-XX)
4 Differential geometry (53-XX)
3 Field theory and polynomials (12-XX)
3 Sequences, series, summability (40-XX)
3 Calculus of variations and optimal control; optimization (49-XX)
3 Manifolds and cell complexes (57-XX)
2 Commutative algebra (13-XX)
2 Category theory; homological algebra (18-XX)
2 Optics, electromagnetic theory (78-XX)
1 Order, lattices, ordered algebraic structures (06-XX)
1 General algebraic systems (08-XX)
1 Algebraic geometry (14-XX)
1 Mechanics of deformable solids (74-XX)
1 Geophysics (86-XX)
1 Mathematics education (97-XX)

Citations by Year

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