## Spitzer, Frank L.

Compute Distance To:
 Author ID: spitzer.frank-l Published as: Spitzer, Frank; Spitzer, F.; Spitzer, Frank L.; Spitzer, F. L. more...less 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 381 Co-Co-Authors
all top 5

### Co-Authors

 32 single-authored 8 Kesten, Harry 2 Liggett, Thomas Milton 2 Ney, Peter E. 2 Widom, Harold 1 Calderon, Alberto Pedro 1 Durrett, Richard Timothy 1 Kozlov, Mykyta V. 1 Meyer, Paul-André 1 Ornstein, Donald Samuel 1 Priouret, Pierre 1 Schmidt, Palle F. 1 Stone, Charles Joel 1 Sznitman, Alain-Sol 1 Wan, Henry jun.
all top 5

### Serials

 5 Transactions of the American Mathematical Society 4 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 3 The Annals of Probability 3 Illinois Journal of Mathematics 3 Proceedings of the American Mathematical Society 3 Bulletin of the American Mathematical Society 2 Advances in Mathematics 2 Duke Mathematical Journal 2 Graduate Texts in Mathematics 1 American Mathematical Monthly 1 Journal d’Analyse Mathématique 1 Journal of Mathematical Analysis and Applications 1 Teoriya Veroyatnosteĭ i eë Primeneniya 1 Acta Mathematica 1 Compositio Mathematica 1 Journal of Functional Analysis 1 Journal of Mathematical Economics 1 Mathematica Scandinavica 1 Journal of Mathematics and Mechanics 1 Lecture Notes in Mathematics 1 Annals of Mathematical Statistics
all top 5

### Fields

 25 Probability theory and stochastic processes (60-XX) 2 Operator theory (47-XX) 1 General and overarching topics; collections (00-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Operations research, mathematical programming (90-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Systems theory; control (93-XX)

### Citations contained in zbMATH Open

46 Publications have been cited 2,292 times in 2,076 Documents Cited by Year
Principles of random walk. Zbl 0119.34304
Spitzer, F.
1964
Interaction of Markov processes. Zbl 0312.60060
Spitzer, Frank
1970
Principles of random walk. 2nd ed. Zbl 0359.60003
Spitzer, Frank
1976
A combinatorial lemma and its application to probability theory. Zbl 0071.13003
Spitzer, Frank
1956
A limit law for random walk in a random environment. Zbl 0388.60069
Kesten, H.; Kozlov, M. V.; Spitzer, F.
1975
Some theorems concerning 2-dimensional Brownian motion. Zbl 0089.13601
Spitzer, Frank
1958
A limit theorem related to a new class of self similar processes. Zbl 0396.60037
Kesten, H.; Spitzer, F.
1979
Markov random fields on an infinite tree. Zbl 0313.60072
Spitzer, Frank
1975
Electrostatic capacity, heat-flow, and Brownian motion. Zbl 0126.33505
Spitzer, F.
1964
Principles of random walk. 2nd ed. 1976, 2nd print. Zbl 0979.60002
Spitzer, Frank
2001
The Toeplitz matrices of an arbitrary Laurent polynomial. Zbl 0101.09203
Schmidt, Palle; Spitzer, Frank
1960
Ergodic theorems for coupled random walks and other systems with locally interacting components. Zbl 0444.60096
Liggett, Thomas M.; Spitzer, Frank
1981
The Wiener-Hopf equation whose kernel is a probability density. Zbl 0082.32003
Spitzer, Frank
1957
The Galton-Watson process with mean one and finite variance. Zbl 0158.35202
Kesten, H.; Ney, P.; Spitzer, F.
1966
Convergence in distribution of products of random matrices. Zbl 0535.60016
Kesten, Harry; Spitzer, Frank
1984
Markov random fields and Gibbs ensembles. Zbl 0241.60094
Spitzer, Frank
1971
On multitype branching processes with $$\rho\leq1$$. Zbl 0178.19504
Joffe, A.; Spitzer, F.
1967
The Martin boundary for random walk. Zbl 0141.15601
Ney, P.; Spitzer, F.
1966
A Tauberian theorem and its probability interpretation. Zbl 0216.21201
Spitzer, F.
1960
Inversion of Toeplitz matrices. Zbl 0091.11101
Calderón, Alberto P.; Spitzer, Frank; Widom, Harold
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
2012
Ratio theorems for random walks. I. Zbl 0121.35201
Kesten, H.; Spitzer, F.
1963
Stochastic time evolution of one dimensional infinite particle systems. Zbl 0372.60149
Spitzer, Frank
1977
The circumference of a convex polygon. Zbl 0099.38501
Spitzer, F.; Widom, H.
1961
A class of Toeplitz forms and their application to probability theory. Zbl 0124.34403
Spitzer, F. L.; Stone, C. J.
1960
Recurrent random walk of an infinite particle system. Zbl 0321.60087
Spitzer, Frank
1974
Random walk on countably infinite Abelian groups. Zbl 0146.38301
Kesten, H.; Spitzer, F.
1965
Random processes defined through the interaction of an infinite particle system. Zbl 0181.43601
Spitzer, F.
1969
A variational characterization of finite Markov chains. Zbl 0238.60093
Spitzer, Frank
1972
The Wiener-Hopf equation whose kernel is a probability density. II. Zbl 0111.30101
Spitzer, F.
1960
Phase transition in one-dimensional nearest-neighbor systems. Zbl 0333.60063
Spitzer, Frank
1975
Hitting probabilities. Zbl 0218.60061
Spitzer, F.
1962
Infinite systems with locally interacting components. Zbl 0462.60096
Spitzer, Frank
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.
1969
Some properties of recurrent random walk. Zbl 0109.36201
Spitzer, F.
1961
Recurrent random walk and logarithmic potential. Zbl 0107.35505
Spitzer, F.
1961
A multidimensional renewal theorem. Zbl 0608.60083
Spitzer, Frank
1986
A general property of random walk. Zbl 0111.32701
Kesten, H.; Ornstein, D.; Spitzer, F.
1962
Controlled Markov chains. Zbl 0318.60070
Kesten, Harry; Spitzer, Frank
1975
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.
1974
Introduction aux processus de Markov à paramètre dans $$\mathbb{Z}_\nu$$. Zbl 0343.60042
Spitzer, Frank L.
1974
The characterization of optimal saving programs in a quadratic model. Zbl 0346.90012
Spitzer, Frank; Wan, Henry jun.
1976
Random time evolution of infinite particle systems. Zbl 0361.60087
Spitzer, Frank
1975
On a class of random variables. Zbl 0064.12803
Spitzer, Frank
1955
Two explicit Martin boundary constructions. Zbl 0158.12802
Spitzer, F.
1967
Renewal theorems for Markov chains. Zbl 0219.60073
Spitzer, F.
1967
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
2012
Principles of random walk. 2nd ed. 1976, 2nd print. Zbl 0979.60002
Spitzer, Frank
2001
A multidimensional renewal theorem. Zbl 0608.60083
Spitzer, Frank
1986
Convergence in distribution of products of random matrices. Zbl 0535.60016
Kesten, Harry; Spitzer, Frank
1984
Ergodic theorems for coupled random walks and other systems with locally interacting components. Zbl 0444.60096
Liggett, Thomas M.; Spitzer, Frank
1981
Infinite systems with locally interacting components. Zbl 0462.60096
Spitzer, Frank
1981
A limit theorem related to a new class of self similar processes. Zbl 0396.60037
Kesten, H.; Spitzer, F.
1979
Stochastic time evolution of one dimensional infinite particle systems. Zbl 0372.60149
Spitzer, Frank
1977
Principles of random walk. 2nd ed. Zbl 0359.60003
Spitzer, Frank
1976
The characterization of optimal saving programs in a quadratic model. Zbl 0346.90012
Spitzer, Frank; Wan, Henry jun.
1976
A limit law for random walk in a random environment. Zbl 0388.60069
Kesten, H.; Kozlov, M. V.; Spitzer, F.
1975
Markov random fields on an infinite tree. Zbl 0313.60072
Spitzer, Frank
1975
Phase transition in one-dimensional nearest-neighbor systems. Zbl 0333.60063
Spitzer, Frank
1975
Controlled Markov chains. Zbl 0318.60070
Kesten, Harry; Spitzer, Frank
1975
Random time evolution of infinite particle systems. Zbl 0361.60087
Spitzer, Frank
1975
Recurrent random walk of an infinite particle system. Zbl 0321.60087
Spitzer, Frank
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.
1974
Introduction aux processus de Markov à paramètre dans $$\mathbb{Z}_\nu$$. Zbl 0343.60042
Spitzer, Frank L.
1974
A variational characterization of finite Markov chains. Zbl 0238.60093
Spitzer, Frank
1972
Markov random fields and Gibbs ensembles. Zbl 0241.60094
Spitzer, Frank
1971
Interaction of Markov processes. Zbl 0312.60060
Spitzer, Frank
1970
Random processes defined through the interaction of an infinite particle system. Zbl 0181.43601
Spitzer, F.
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.
1969
On multitype branching processes with $$\rho\leq1$$. Zbl 0178.19504
Joffe, A.; Spitzer, F.
1967
Two explicit Martin boundary constructions. Zbl 0158.12802
Spitzer, F.
1967
Renewal theorems for Markov chains. Zbl 0219.60073
Spitzer, F.
1967
The Galton-Watson process with mean one and finite variance. Zbl 0158.35202
Kesten, H.; Ney, P.; Spitzer, F.
1966
The Martin boundary for random walk. Zbl 0141.15601
Ney, P.; Spitzer, F.
1966
Random walk on countably infinite Abelian groups. Zbl 0146.38301
Kesten, H.; Spitzer, F.
1965
Principles of random walk. Zbl 0119.34304
Spitzer, F.
1964
Electrostatic capacity, heat-flow, and Brownian motion. Zbl 0126.33505
Spitzer, F.
1964
Ratio theorems for random walks. I. Zbl 0121.35201
Kesten, H.; Spitzer, F.
1963
Hitting probabilities. Zbl 0218.60061
Spitzer, F.
1962
A general property of random walk. Zbl 0111.32701
Kesten, H.; Ornstein, D.; Spitzer, F.
1962
The circumference of a convex polygon. Zbl 0099.38501
Spitzer, F.; Widom, H.
1961
Some properties of recurrent random walk. Zbl 0109.36201
Spitzer, F.
1961
Recurrent random walk and logarithmic potential. Zbl 0107.35505
Spitzer, F.
1961
The Toeplitz matrices of an arbitrary Laurent polynomial. Zbl 0101.09203
Schmidt, Palle; Spitzer, Frank
1960
A Tauberian theorem and its probability interpretation. Zbl 0216.21201
Spitzer, F.
1960
A class of Toeplitz forms and their application to probability theory. Zbl 0124.34403
Spitzer, F. L.; Stone, C. J.
1960
The Wiener-Hopf equation whose kernel is a probability density. II. Zbl 0111.30101
Spitzer, F.
1960
Inversion of Toeplitz matrices. Zbl 0091.11101
Calderón, Alberto P.; Spitzer, Frank; Widom, Harold
1959
Some theorems concerning 2-dimensional Brownian motion. Zbl 0089.13601
Spitzer, Frank
1958
The Wiener-Hopf equation whose kernel is a probability density. Zbl 0082.32003
Spitzer, Frank
1957
A combinatorial lemma and its application to probability theory. Zbl 0071.13003
Spitzer, Frank
1956
On a class of random variables. Zbl 0064.12803
Spitzer, Frank
1955
all top 5

### Cited by 2,068 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 Souissi, Abdessatar 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 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 1,968 more Authors
all top 5

### Cited in 341 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 17 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 Quantum Information Processing 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 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 241 more Serials
all top 5

### Cited in 55 Fields

 1,584 Probability theory and stochastic processes (60-XX) 451 Statistical mechanics, structure of matter (82-XX) 127 Combinatorics (05-XX) 95 Statistics (62-XX) 73 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) 44 Computer science (68-XX) 42 Quantum theory (81-XX) 41 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 40 Measure and integration (28-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)

### Wikidata Timeline

The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.