Edit Profile (opens in new tab) Spitzer, Frank L. (b. 1926 d. 1992) Co-Author Distance 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 403 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 47 Publications have been cited 2,575 times in 2,330 Documents Cited by ▼ Year ▼ Principles of random walk. Zbl 0119.34304 Spitzer, F. 445 1964 Interaction of Markov processes. Zbl 0312.60060 Spitzer, Frank 326 1970 Principles of random walk. 2nd ed. Zbl 0359.60003 Spitzer, Frank 269 1976 A combinatorial lemma and its application to probability theory. Zbl 0071.13003 Spitzer, Frank 262 1956 A limit law for random walk in a random environment. Zbl 0388.60069 Kesten, H.; Kozlov, M. V.; Spitzer, F. 185 1975 Some theorems concerning 2-dimensional Brownian motion. Zbl 0089.13601 Spitzer, Frank 127 1958 A limit theorem related to a new class of self similar processes. Zbl 0396.60037 Kesten, H.; Spitzer, F. 112 1979 Markov random fields on an infinite tree. Zbl 0313.60072 Spitzer, Frank 93 1975 Principles of random walk. 2nd ed. 1976, 2nd print. Zbl 0979.60002 Spitzer, Frank 73 2001 Electrostatic capacity, heat-flow, and Brownian motion. Zbl 0126.33505 Spitzer, F. 70 1964 The Toeplitz matrices of an arbitrary Laurent polynomial. Zbl 0101.09203 Schmidt, Palle; Spitzer, Frank 53 1960 The Wiener-Hopf equation whose kernel is a probability density. Zbl 0082.32003 Spitzer, Frank 46 1957 The Galton-Watson process with mean one and finite variance. Zbl 0158.35202 Kesten, H.; Ney, P.; Spitzer, F. 43 1966 Ergodic theorems for coupled random walks and other systems with locally interacting components. Zbl 0444.60096 Liggett, Thomas M.; Spitzer, Frank 43 1981 Convergence in distribution of products of random matrices. Zbl 0535.60016 Kesten, Harry; Spitzer, Frank 39 1984 A Tauberian theorem and its probability interpretation. Zbl 0216.21201 Spitzer, F. 38 1960 Markov random fields and Gibbs ensembles. Zbl 0241.60094 Spitzer, Frank 38 1971 On multitype branching processes with \(\rho\leq1\). Zbl 0178.19504 Joffe, A.; Spitzer, F. 36 1967 The Martin boundary for random walk. Zbl 0141.15601 Ney, P.; Spitzer, F. 35 1966 Inversion of Toeplitz matrices. Zbl 0091.11101 Calderón, Alberto P.; Spitzer, Frank; Widom, Harold 31 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 20 2012 Stochastic time evolution of one dimensional infinite particle systems. Zbl 0372.60149 Spitzer, Frank 17 1977 The circumference of a convex polygon. Zbl 0099.38501 Spitzer, F.; Widom, H. 16 1961 Ratio theorems for random walks. I. Zbl 0121.35201 Kesten, H.; Spitzer, F. 16 1963 Random walk on countably infinite Abelian groups. Zbl 0146.38301 Kesten, H.; Spitzer, F. 16 1965 A class of Toeplitz forms and their application to probability theory. Zbl 0124.34403 Spitzer, F. L.; Stone, C. J. 15 1960 Recurrent random walk of an infinite particle system. Zbl 0321.60087 Spitzer, Frank 13 1974 Random processes defined through the interaction of an infinite particle system. Zbl 0181.43601 Spitzer, F. 13 1969 A variational characterization of finite Markov chains. Zbl 0238.60093 Spitzer, Frank 12 1972 The Wiener-Hopf equation whose kernel is a probability density. II. Zbl 0111.30101 Spitzer, F. 12 1960 Phase transition in one-dimensional nearest-neighbor systems. Zbl 0333.60063 Spitzer, Frank 10 1975 Hitting probabilities. Zbl 0218.60061 Spitzer, F. 8 1962 Infinite systems with locally interacting components. Zbl 0462.60096 Spitzer, Frank 7 1981 Recurrent random walk and logarithmic potential. Zbl 0107.35505 Spitzer, F. 6 1961 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 A multidimensional renewal theorem. Zbl 0608.60083 Spitzer, Frank 4 1986 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. 3 1974 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 Introduction aux processus de Markov à paramètre dans \(\mathbb{Z}_\nu\). Zbl 0343.60042 Spitzer, Frank L. 2 1974 Renewal theorems for Markov chains. Zbl 0219.60073 Spitzer, F. 1 1967 On a class of random variables. Zbl 0064.12803 Spitzer, Frank 1 1955 On interval recurrent sums of independent random variables. Zbl 0070.13802 Spitzer, Frank 1 1956 Two explicit Martin boundary constructions. Zbl 0158.12802 Spitzer, F. 1 1967 The characterization of optimal saving programs in a quadratic model. Zbl 0346.90012 Spitzer, Frank; Wan, Henry jun. 1 1976 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 20 2012 Principles of random walk. 2nd ed. 1976, 2nd print. Zbl 0979.60002 Spitzer, Frank 73 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 39 1984 Ergodic theorems for coupled random walks and other systems with locally interacting components. Zbl 0444.60096 Liggett, Thomas M.; Spitzer, Frank 43 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. 112 1979 Stochastic time evolution of one dimensional infinite particle systems. Zbl 0372.60149 Spitzer, Frank 17 1977 Principles of random walk. 2nd ed. Zbl 0359.60003 Spitzer, Frank 269 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. 185 1975 Markov random fields on an infinite tree. Zbl 0313.60072 Spitzer, Frank 93 1975 Phase transition in one-dimensional nearest-neighbor systems. Zbl 0333.60063 Spitzer, Frank 10 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. 3 1974 Introduction aux processus de Markov à paramètre dans \(\mathbb{Z}_\nu\). Zbl 0343.60042 Spitzer, Frank L. 2 1974 A variational characterization of finite Markov chains. Zbl 0238.60093 Spitzer, Frank 12 1972 Markov random fields and Gibbs ensembles. Zbl 0241.60094 Spitzer, Frank 38 1971 Interaction of Markov processes. Zbl 0312.60060 Spitzer, Frank 326 1970 Random processes defined through the interaction of an infinite particle system. Zbl 0181.43601 Spitzer, F. 13 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. 36 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. 43 1966 The Martin boundary for random walk. Zbl 0141.15601 Ney, P.; Spitzer, F. 35 1966 Random walk on countably infinite Abelian groups. Zbl 0146.38301 Kesten, H.; Spitzer, F. 16 1965 Principles of random walk. Zbl 0119.34304 Spitzer, F. 445 1964 Electrostatic capacity, heat-flow, and Brownian motion. Zbl 0126.33505 Spitzer, F. 70 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. 16 1961 Recurrent random walk and logarithmic potential. Zbl 0107.35505 Spitzer, F. 6 1961 Some properties of recurrent random walk. Zbl 0109.36201 Spitzer, F. 5 1961 The Toeplitz matrices of an arbitrary Laurent polynomial. Zbl 0101.09203 Schmidt, Palle; Spitzer, Frank 53 1960 A Tauberian theorem and its probability interpretation. Zbl 0216.21201 Spitzer, F. 38 1960 A class of Toeplitz forms and their application to probability theory. Zbl 0124.34403 Spitzer, F. L.; Stone, C. J. 15 1960 The Wiener-Hopf equation whose kernel is a probability density. II. Zbl 0111.30101 Spitzer, F. 12 1960 Inversion of Toeplitz matrices. Zbl 0091.11101 Calderón, Alberto P.; Spitzer, Frank; Widom, Harold 31 1959 Some theorems concerning 2-dimensional Brownian motion. Zbl 0089.13601 Spitzer, Frank 127 1958 The Wiener-Hopf equation whose kernel is a probability density. Zbl 0082.32003 Spitzer, Frank 46 1957 A combinatorial lemma and its application to probability theory. Zbl 0071.13003 Spitzer, Frank 262 1956 On interval recurrent sums of independent random variables. Zbl 0070.13802 Spitzer, Frank 1 1956 On a class of random variables. Zbl 0064.12803 Spitzer, Frank 1 1955 all cited Publications top 5 cited Publications all top 5 Cited by 2,362 Authors 26 den Hollander, Frank 21 Csáki, Endre 21 Majumdar, Satya N. 19 Uchiyama, Kôhei 17 Spitzer, Frank L. 17 van den Berg, Michiel 16 Peres, Yuval 16 Révész, Pál 15 Liggett, Thomas Milton 15 Rozikov, Utkir A. 15 Schehr, Grégory 14 Böttcher, Albrecht 14 Mukhamedov, Farruh Maksutovich 13 Földes, Antónia 13 Gantert, Nina 13 Greven, Andreas 13 Shi, Zhan 13 Yor, Marc 12 Godrèche, Claude 12 Guillotin-Plantard, Nadine 12 Kesten, Harry 12 Pène, Françoise 12 Vatutin, Vladimir Alekseevich 11 Buraczewski, Dariusz 11 Dolgopyat, Dmitry 11 Doney, Ronald Arthur 11 Ferrari, Pablo Augusto 11 Großkinsky, Stefan 11 Khoshnevisan, Davar 11 Le Gall, Jean-François 11 Petrov, Leonid 11 Seppäläinen, Timo 10 Borodin, Alexei 10 Cox, J. Theodore 10 Gonçalves, Patrícia C. 10 Gut, Allan 10 Peterson, Jonathon 10 Schütz, Gunter M. 10 Sznitman, Alain-Sol 10 Wade, Andrew R. 10 Widom, Harold 9 Afanas’ev, Valeriĭ Ivanovich 9 D’yakonova, Elena Evgen’evna 9 Jain, Naresh C. 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 Cygan, Wojciech 8 Deuschel, Jean-Dominique 8 Durrett, Richard Timothy 8 Ebrahimi-Fard, Kurusch 8 Fribergh, Alexander 8 Goldsheid, Ilya Ya. 8 Grudsky, Sergei Mikhailovich 8 Hu, Yueyun 8 Sandrić, Nikola 8 Song, Renming 7 Balazs, Marton 7 Baxter, Glen Earl 7 Benjamini, Itai 7 Bolthausen, Erwin 7 Comets, Francis M. 7 Corteel, Sylvie 7 Guivarc’h, Yves 7 Hamana, Yuji 7 Haydarov, Farhod Halimjonovich 7 Lawler, Gregory Francis 7 Lebowitz, Joel Louis 7 Liu, Quansheng 7 Lopes, Artur Oscar 7 Luck, Jean-Marc 7 Mandelshtam, Olya 7 Menshikov, Mikhail V. 7 Port, Sidney Charles 7 Rassoul-Agha, Firas 7 Salez, Justin 7 Saloff-Coste, Laurent 7 Šebek, Stjepan 7 Souissi, Abdessatar 7 van Leeuwaarden, Johan S. H. 7 Vysotsky, Vladislav V. 7 Williams, Lauren K. 6 Bendikov, Alexander D. 6 Csörgő, Miklós 6 Dawson, Donald Andrew 6 Enriquez, Nathanaël 6 Erschler, Anna 6 Eshkabilov, Yusup Khalbaevich 6 Fleischmann, Klaus 6 Ganikhodjaev, Nasir Nabievich 6 Grama, Ion G. 6 Iksanov, Aleksander M. 6 Jara, Milton D. 6 König, Wolfgang Dieter 6 Konno, Norio 6 Le Jan, Yves ...and 2,262 more Authors all top 5 Cited in 371 Serials 163 Stochastic Processes and their Applications 124 Journal of Statistical Physics 124 Probability Theory and Related Fields 117 The Annals of Probability 105 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 66 Journal of Statistical Mechanics: Theory and Experiment 65 Journal of Theoretical Probability 61 Electronic Journal of Probability 59 Transactions of the American Mathematical Society 59 Statistics & Probability Letters 53 Communications in Mathematical Physics 45 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 43 Journal of Mathematical Analysis and Applications 39 The Annals of Applied Probability 37 Journal of Physics A: Mathematical and Theoretical 22 Proceedings of the American Mathematical Society 21 Potential Analysis 19 Journal of Functional Analysis 18 Advances in Applied Probability 18 Electronic Communications in Probability 17 Journal d’Analyse Mathématique 17 ALEA. Latin American Journal of Probability and Mathematical Statistics 16 Advances in Mathematics 15 Journal of Applied Probability 15 Journal of Soviet Mathematics 15 Mathematical Physics, Analysis and Geometry 13 Annales de l’Institut Fourier 12 Israel Journal of Mathematics 12 Journal of Multivariate Analysis 12 Annales de l’Institut Henri Poincaré. Nouvelle Série. Section B. Calcul des Probabilités et Statistique 12 Linear Algebra and its Applications 11 Ukrainian Mathematical Journal 11 Bernoulli 11 Acta Mathematica Sinica. English Series 11 Bulletin of the American Mathematical Society 10 Theoretical and Mathematical Physics 10 Communications in Statistics. Theory and Methods 10 Journal of the Australian Mathematical Society 9 Journal of Mathematical Physics 9 Lithuanian Mathematical Journal 9 Comptes Rendus. Mathématique. Académie des Sciences, Paris 8 Mathematical Notes 8 Siberian Mathematical Journal 8 Advances in Applied Mathematics 8 Journal of Mathematical Sciences (New York) 8 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 7 Journal of Mathematical Biology 7 Mathematical Biosciences 7 Physica A 7 Theory of Probability and its Applications 7 Integral Equations and Operator Theory 7 Acta Mathematica Hungarica 7 Acta Applicandae Mathematicae 7 Random Structures & Algorithms 7 Quantum Information Processing 7 Frontiers of Mathematics in China 7 Probability Surveys 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 Queueing Systems 6 Proceedings of the Steklov Institute of Mathematics 5 Communications on Pure and Applied Mathematics 5 Letters in Mathematical Physics 5 Nonlinearity 5 Periodica Mathematica Hungarica 5 Arkiv för Matematik 5 Acta Mathematica 5 Bulletin de la Société Mathématique de France 5 Journal of Combinatorial Theory. Series A 5 Journal of Computational and Applied Mathematics 5 Journal of Statistical Planning and Inference 5 Mathematische Nachrichten 5 Theoretical Population Biology 5 Ergodic Theory and Dynamical Systems 5 Discrete Mathematics and Applications 5 Bulletin of the American Mathematical Society. New Series 5 Combinatorics, Probability and Computing 5 The Electronic Journal of Combinatorics 5 Journal of Inequalities and Applications 5 Stochastics and Dynamics 5 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 5 Science China. Mathematics 5 Annales Henri Lebesgue 4 Computers & Mathematics with Applications 4 Discrete Mathematics 4 Mathematical Proceedings of the Cambridge Philosophical Society 4 Annales Scientifiques de l’Université de Clermont-Ferrand II. Mathématiques 4 Journal of Approximation Theory 4 Mathematische Zeitschrift 4 Journal of Time Series Analysis 4 Constructive Approximation 4 Acta Mathematica Sinica. New Series 4 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 4 Mathematical Methods of Statistics ...and 271 more Serials all top 5 Cited in 56 Fields 1,753 Probability theory and stochastic processes (60-XX) 550 Statistical mechanics, structure of matter (82-XX) 149 Combinatorics (05-XX) 113 Statistics (62-XX) 90 Partial differential equations (35-XX) 89 Dynamical systems and ergodic theory (37-XX) 72 Operator theory (47-XX) 67 Biology and other natural sciences (92-XX) 64 Linear and multilinear algebra; matrix theory (15-XX) 55 Quantum theory (81-XX) 52 Numerical analysis (65-XX) 52 Computer science (68-XX) 44 Measure and integration (28-XX) 42 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 41 Potential theory (31-XX) 36 Operations research, mathematical programming (90-XX) 28 Functional analysis (46-XX) 22 Number theory (11-XX) 21 Harmonic analysis on Euclidean spaces (42-XX) 20 Group theory and generalizations (20-XX) 19 Integral equations (45-XX) 18 Functions of a complex variable (30-XX) 17 Special functions (33-XX) 16 Approximations and expansions (41-XX) 15 Abstract harmonic analysis (43-XX) 14 Nonassociative rings and algebras (17-XX) 14 Global analysis, analysis on manifolds (58-XX) 14 Systems theory; control (93-XX) 13 Topological groups, Lie groups (22-XX) 12 Ordinary differential equations (34-XX) 12 Information and communication theory, circuits (94-XX) 11 Associative rings and algebras (16-XX) 10 Convex and discrete geometry (52-XX) 10 Fluid mechanics (76-XX) 9 Real functions (26-XX) 8 History and biography (01-XX) 6 Integral transforms, operational calculus (44-XX) 6 Classical thermodynamics, heat transfer (80-XX) 4 Mathematical logic and foundations (03-XX) 4 Difference and functional equations (39-XX) 4 Differential geometry (53-XX) 4 Mechanics of particles and systems (70-XX) 4 Optics, electromagnetic theory (78-XX) 3 General and overarching topics; collections (00-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) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Algebraic geometry (14-XX) 1 Geometry (51-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.