Edit Profile (opens in new tab) Spitzer, Frank L. Compute Distance To: Compute 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) Publications by Year all cited Publications top 5 cited Publications 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 0119.34304Spitzer, F. 396 1964 Interaction of Markov processes. Zbl 0312.60060Spitzer, Frank 269 1970 Principles of random walk. 2nd ed. Zbl 0359.60003Spitzer, Frank 238 1976 A combinatorial lemma and its application to probability theory. Zbl 0071.13003Spitzer, Frank 238 1956 A limit law for random walk in a random environment. Zbl 0388.60069Kesten, H.; Kozlov, M. V.; Spitzer, F. 168 1975 Some theorems concerning 2-dimensional Brownian motion. Zbl 0089.13601Spitzer, Frank 113 1958 A limit theorem related to a new class of self similar processes. Zbl 0396.60037Kesten, H.; Spitzer, F. 106 1979 Markov random fields on an infinite tree. Zbl 0313.60072Spitzer, Frank 82 1975 Electrostatic capacity, heat-flow, and Brownian motion. Zbl 0126.33505Spitzer, F. 69 1964 Principles of random walk. 2nd ed. 1976, 2nd print. Zbl 0979.60002Spitzer, Frank 59 2001 The Toeplitz matrices of an arbitrary Laurent polynomial. Zbl 0101.09203Schmidt, Palle; Spitzer, Frank 51 1960 Ergodic theorems for coupled random walks and other systems with locally interacting components. Zbl 0444.60096Liggett, Thomas M.; Spitzer, Frank 41 1981 The Wiener-Hopf equation whose kernel is a probability density. Zbl 0082.32003Spitzer, Frank 40 1957 The Galton-Watson process with mean one and finite variance. Zbl 0158.35202Kesten, H.; Ney, P.; Spitzer, F. 38 1966 Convergence in distribution of products of random matrices. Zbl 0535.60016Kesten, Harry; Spitzer, Frank 35 1984 Markov random fields and Gibbs ensembles. Zbl 0241.60094Spitzer, Frank 35 1971 On multitype branching processes with \(\rho\leq1\). Zbl 0178.19504Joffe, A.; Spitzer, F. 34 1967 The Martin boundary for random walk. Zbl 0141.15601Ney, P.; Spitzer, F. 33 1966 A Tauberian theorem and its probability interpretation. Zbl 0216.21201Spitzer, F. 31 1960 Inversion of Toeplitz matrices. Zbl 0091.11101Calderón, 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 1248.82021Durrett, Rick; Liggett, Thomas M.; Spitzer, Frank; Sznitman, Alain-Sol 18 2012 Ratio theorems for random walks. I. Zbl 0121.35201Kesten, H.; Spitzer, F. 16 1963 Stochastic time evolution of one dimensional infinite particle systems. Zbl 0372.60149Spitzer, Frank 16 1977 The circumference of a convex polygon. Zbl 0099.38501Spitzer, F.; Widom, H. 15 1961 A class of Toeplitz forms and their application to probability theory. Zbl 0124.34403Spitzer, F. L.; Stone, C. J. 14 1960 Recurrent random walk of an infinite particle system. Zbl 0321.60087Spitzer, Frank 13 1974 Random walk on countably infinite Abelian groups. Zbl 0146.38301Kesten, H.; Spitzer, F. 13 1965 Random processes defined through the interaction of an infinite particle system. Zbl 0181.43601Spitzer, F. 11 1969 A variational characterization of finite Markov chains. Zbl 0238.60093Spitzer, Frank 10 1972 The Wiener-Hopf equation whose kernel is a probability density. II. Zbl 0111.30101Spitzer, F. 9 1960 Phase transition in one-dimensional nearest-neighbor systems. Zbl 0333.60063Spitzer, Frank 9 1975 Hitting probabilities. Zbl 0218.60061Spitzer, F. 8 1962 Infinite systems with locally interacting components. Zbl 0462.60096Spitzer, 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 0175.16702Spitzer, F. 6 1969 Some properties of recurrent random walk. Zbl 0109.36201Spitzer, F. 5 1961 Recurrent random walk and logarithmic potential. Zbl 0107.35505Spitzer, F. 4 1961 A multidimensional renewal theorem. Zbl 0608.60083Spitzer, Frank 4 1986 A general property of random walk. Zbl 0111.32701Kesten, H.; Ornstein, D.; Spitzer, F. 2 1962 Controlled Markov chains. Zbl 0318.60070Kesten, Harry; Spitzer, Frank 2 1975 Ecole d’ete de probabilites de Saint-Flour III - 1973. Edite par A. Badrikian et P.-L. Hennequin. Zbl 0277.00014Meyer, P. A.; Priouret, P.; Spitzer, F. 1 1974 Introduction aux processus de Markov à paramètre dans \(\mathbb{Z}_\nu\). Zbl 0343.60042Spitzer, Frank L. 1 1974 The characterization of optimal saving programs in a quadratic model. Zbl 0346.90012Spitzer, Frank; Wan, Henry jun. 1 1976 Random time evolution of infinite particle systems. Zbl 0361.60087Spitzer, Frank 1 1975 On a class of random variables. Zbl 0064.12803Spitzer, Frank 1 1955 Two explicit Martin boundary constructions. Zbl 0158.12802Spitzer, F. 1 1967 Renewal theorems for Markov chains. Zbl 0219.60073Spitzer, F. 1 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 1248.82021Durrett, Rick; Liggett, Thomas M.; Spitzer, Frank; Sznitman, Alain-Sol 18 2012 Principles of random walk. 2nd ed. 1976, 2nd print. Zbl 0979.60002Spitzer, Frank 59 2001 A multidimensional renewal theorem. Zbl 0608.60083Spitzer, Frank 4 1986 Convergence in distribution of products of random matrices. Zbl 0535.60016Kesten, Harry; Spitzer, Frank 35 1984 Ergodic theorems for coupled random walks and other systems with locally interacting components. Zbl 0444.60096Liggett, Thomas M.; Spitzer, Frank 41 1981 Infinite systems with locally interacting components. Zbl 0462.60096Spitzer, Frank 7 1981 A limit theorem related to a new class of self similar processes. Zbl 0396.60037Kesten, H.; Spitzer, F. 106 1979 Stochastic time evolution of one dimensional infinite particle systems. Zbl 0372.60149Spitzer, Frank 16 1977 Principles of random walk. 2nd ed. Zbl 0359.60003Spitzer, Frank 238 1976 The characterization of optimal saving programs in a quadratic model. Zbl 0346.90012Spitzer, Frank; Wan, Henry jun. 1 1976 A limit law for random walk in a random environment. Zbl 0388.60069Kesten, H.; Kozlov, M. V.; Spitzer, F. 168 1975 Markov random fields on an infinite tree. Zbl 0313.60072Spitzer, Frank 82 1975 Phase transition in one-dimensional nearest-neighbor systems. Zbl 0333.60063Spitzer, Frank 9 1975 Controlled Markov chains. Zbl 0318.60070Kesten, Harry; Spitzer, Frank 2 1975 Random time evolution of infinite particle systems. Zbl 0361.60087Spitzer, Frank 1 1975 Recurrent random walk of an infinite particle system. Zbl 0321.60087Spitzer, Frank 13 1974 Ecole d’ete de probabilites de Saint-Flour III - 1973. Edite par A. Badrikian et P.-L. Hennequin. Zbl 0277.00014Meyer, P. A.; Priouret, P.; Spitzer, F. 1 1974 Introduction aux processus de Markov à paramètre dans \(\mathbb{Z}_\nu\). Zbl 0343.60042Spitzer, Frank L. 1 1974 A variational characterization of finite Markov chains. Zbl 0238.60093Spitzer, Frank 10 1972 Markov random fields and Gibbs ensembles. Zbl 0241.60094Spitzer, Frank 35 1971 Interaction of Markov processes. Zbl 0312.60060Spitzer, Frank 269 1970 Random processes defined through the interaction of an infinite particle system. Zbl 0181.43601Spitzer, 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 0175.16702Spitzer, F. 6 1969 On multitype branching processes with \(\rho\leq1\). Zbl 0178.19504Joffe, A.; Spitzer, F. 34 1967 Two explicit Martin boundary constructions. Zbl 0158.12802Spitzer, F. 1 1967 Renewal theorems for Markov chains. Zbl 0219.60073Spitzer, F. 1 1967 The Galton-Watson process with mean one and finite variance. Zbl 0158.35202Kesten, H.; Ney, P.; Spitzer, F. 38 1966 The Martin boundary for random walk. Zbl 0141.15601Ney, P.; Spitzer, F. 33 1966 Random walk on countably infinite Abelian groups. Zbl 0146.38301Kesten, H.; Spitzer, F. 13 1965 Principles of random walk. Zbl 0119.34304Spitzer, F. 396 1964 Electrostatic capacity, heat-flow, and Brownian motion. Zbl 0126.33505Spitzer, F. 69 1964 Ratio theorems for random walks. I. Zbl 0121.35201Kesten, H.; Spitzer, F. 16 1963 Hitting probabilities. Zbl 0218.60061Spitzer, F. 8 1962 A general property of random walk. Zbl 0111.32701Kesten, H.; Ornstein, D.; Spitzer, F. 2 1962 The circumference of a convex polygon. Zbl 0099.38501Spitzer, F.; Widom, H. 15 1961 Some properties of recurrent random walk. Zbl 0109.36201Spitzer, F. 5 1961 Recurrent random walk and logarithmic potential. Zbl 0107.35505Spitzer, F. 4 1961 The Toeplitz matrices of an arbitrary Laurent polynomial. Zbl 0101.09203Schmidt, Palle; Spitzer, Frank 51 1960 A Tauberian theorem and its probability interpretation. Zbl 0216.21201Spitzer, F. 31 1960 A class of Toeplitz forms and their application to probability theory. Zbl 0124.34403Spitzer, F. L.; Stone, C. J. 14 1960 The Wiener-Hopf equation whose kernel is a probability density. II. Zbl 0111.30101Spitzer, F. 9 1960 Inversion of Toeplitz matrices. Zbl 0091.11101Calderón, Alberto P.; Spitzer, Frank; Widom, Harold 27 1959 Some theorems concerning 2-dimensional Brownian motion. Zbl 0089.13601Spitzer, Frank 113 1958 The Wiener-Hopf equation whose kernel is a probability density. Zbl 0082.32003Spitzer, Frank 40 1957 A combinatorial lemma and its application to probability theory. Zbl 0071.13003Spitzer, Frank 238 1956 On a class of random variables. Zbl 0064.12803Spitzer, Frank 1 1955 all cited Publications top 5 cited Publications 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) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.