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Spitzer, Frank L. (b. 1926 d. 1992)

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
403 Co-Co-Authors

Publications by Year

Citations contained in zbMATH Open

47 Publications have been cited 2,636 times in 2,383 Documents Cited by Year
Principles of random walk. Zbl 0119.34304
Spitzer, F.
449
1964
Interaction of Markov processes. Zbl 0312.60060
Spitzer, Frank
336
1970
Principles of random walk. 2nd ed. Zbl 0359.60003
Spitzer, Frank
283
1976
A combinatorial lemma and its application to probability theory. Zbl 0071.13003
Spitzer, Frank
267
1956
A limit law for random walk in a random environment. Zbl 0388.60069
Kesten, H.; Kozlov, M. V.; Spitzer, F.
189
1975
Some theorems concerning 2-dimensional Brownian motion. Zbl 0089.13601
Spitzer, Frank
132
1958
A limit theorem related to a new class of self similar processes. Zbl 0396.60037
Kesten, H.; Spitzer, F.
114
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
74
2001
Electrostatic capacity, heat-flow, and Brownian motion. Zbl 0126.33505
Spitzer, F.
72
1964
The Toeplitz matrices of an arbitrary Laurent polynomial. Zbl 0101.09203
Schmidt, Palle; Spitzer, Frank
56
1960
The Wiener-Hopf equation whose kernel is a probability density. Zbl 0082.32003
Spitzer, Frank
48
1957
The Galton-Watson process with mean one and finite variance. Zbl 0158.35202
Kesten, H.; Ney, P.; Spitzer, F.
44
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
Markov random fields and Gibbs ensembles. Zbl 0241.60094
Spitzer, Frank
39
1971
A Tauberian theorem and its probability interpretation. Zbl 0216.21201
Spitzer, F.
38
1960
On multitype branching processes with \(\rho\leq1\). Zbl 0178.19504
Joffe, A.; Spitzer, F.
37
1967
The Martin boundary for random walk. Zbl 0141.15601
Ney, P.; Spitzer, F.
36
1966
Inversion of Toeplitz matrices. Zbl 0091.11101
Calderón, Alberto P.; Spitzer, Frank; Widom, Harold
33
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
Random walk on countably infinite Abelian groups. Zbl 0146.38301
Kesten, H.; Spitzer, F.
16
1965
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
A class of Toeplitz forms and their application to probability theory. Zbl 0124.34403
Spitzer, F. L.; Stone, C. J.
15
1960
Random processes defined through the interaction of an infinite particle system. Zbl 0181.43601
Spitzer, F.
13
1969
Recurrent random walk of an infinite particle system. Zbl 0321.60087
Spitzer, Frank
13
1974
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
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
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
A multidimensional renewal theorem. Zbl 0608.60083
Spitzer, Frank
4
1986
Introduction aux processus de Markov à paramètre dans \(\mathbb{Z}_\nu\). Zbl 0343.60042
Spitzer, Frank L.
4
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
Controlled Markov chains. Zbl 0318.60070
Kesten, Harry; Spitzer, Frank
3
1975
A general property of random walk. Zbl 0111.32701
Kesten, H.; Ornstein, D.; Spitzer, F.
2
1962
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
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
Renewal theorems for Markov chains. Zbl 0219.60073
Spitzer, 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 1248.82021
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
74
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.
114
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
283
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.
189
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
3
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
Introduction aux processus de Markov à paramètre dans \(\mathbb{Z}_\nu\). Zbl 0343.60042
Spitzer, Frank L.
4
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
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
39
1971
Interaction of Markov processes. Zbl 0312.60060
Spitzer, Frank
336
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.
37
1967
Two explicit Martin boundary constructions. Zbl 0158.12802
Spitzer, F.
1
1967
Renewal theorems for Markov chains. Zbl 0219.60073
Spitzer, F.
1
1967
The Galton-Watson process with mean one and finite variance. Zbl 0158.35202
Kesten, H.; Ney, P.; Spitzer, F.
44
1966
The Martin boundary for random walk. Zbl 0141.15601
Ney, P.; Spitzer, F.
36
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.
449
1964
Electrostatic capacity, heat-flow, and Brownian motion. Zbl 0126.33505
Spitzer, F.
72
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
56
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
33
1959
Some theorems concerning 2-dimensional Brownian motion. Zbl 0089.13601
Spitzer, Frank
132
1958
The Wiener-Hopf equation whose kernel is a probability density. Zbl 0082.32003
Spitzer, Frank
48
1957
A combinatorial lemma and its application to probability theory. Zbl 0071.13003
Spitzer, Frank
267
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 top 5

Cited by 2,412 Authors

26 den Hollander, Frank
23 Majumdar, Satya N.
21 Csáki, Endre
20 Uchiyama, Kôhei
17 Spitzer, Frank L.
17 van den Berg, Michiel
16 Peres, Yuval
16 Révész, Pál
16 Schehr, Grégory
15 Böttcher, Albrecht
15 Liggett, Thomas Milton
15 Rozikov, Utkir A.
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 Borodin, Alexei
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 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 Corwin, Ivan Z.
9 D’yakonova, Elena Evgen’evna
9 Ebrahimi-Fard, Kurusch
9 Grudsky, Sergei Mikhailovich
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 Cygan, Wojciech
8 Deuschel, Jean-Dominique
8 Durrett, Richard Timothy
8 Fribergh, Alexander
8 Goldsheid, Ilya Ya.
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 Ignatiouk-Robert, Irina
6 Iksanov, Aleksander M.
6 Jara, Milton D.
6 König, Wolfgang Dieter
6 Konno, Norio
...and 2,312 more Authors
all top 5

Cited in 377 Serials

168 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
63 Electronic Journal of Probability
59 Transactions of the American Mathematical Society
59 Statistics & Probability Letters
54 Communications in Mathematical Physics
48 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques
44 Journal of Mathematical Analysis and Applications
41 The Annals of Applied Probability
41 Journal of Physics A: Mathematical and Theoretical
22 Proceedings of the American Mathematical Society
21 Potential Analysis
20 Journal of Functional Analysis
18 Advances in Applied Probability
18 Electronic Communications in Probability
17 Journal d’Analyse Mathématique
17 Advances in Mathematics
17 ALEA. Latin American Journal of Probability and Mathematical Statistics
15 Journal of Applied Probability
15 Journal of Soviet Mathematics
15 Mathematical Physics, Analysis and Geometry
13 Annales de l’Institut Fourier
13 Journal of Multivariate Analysis
12 Israel Journal of Mathematics
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 Physica A
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 Random Structures & Algorithms
9 Comptes Rendus. Mathématique. Académie des Sciences, Paris
8 Mathematical Biosciences
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 Theory of Probability and its Applications
7 Integral Equations and Operator Theory
7 Theoretical Computer Science
7 Acta Mathematica Hungarica
7 Acta Applicandae Mathematicae
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 Journal of Computational and Applied Mathematics
6 Mathematische Nachrichten
6 Monatshefte für Mathematik
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 Statistical Planning and Inference
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 Methodology and Computing in Applied Probability
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 Reports on Mathematical Physics
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
...and 277 more Serials
all top 5

Cited in 57 Fields

1,793 Probability theory and stochastic processes (60-XX)
563 Statistical mechanics, structure of matter (82-XX)
154 Combinatorics (05-XX)
115 Statistics (62-XX)
93 Partial differential equations (35-XX)
91 Dynamical systems and ergodic theory (37-XX)
75 Operator theory (47-XX)
69 Linear and multilinear algebra; matrix theory (15-XX)
68 Biology and other natural sciences (92-XX)
55 Quantum theory (81-XX)
54 Computer science (68-XX)
53 Numerical analysis (65-XX)
44 Measure and integration (28-XX)
44 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
42 Potential theory (31-XX)
36 Operations research, mathematical programming (90-XX)
29 Functional analysis (46-XX)
26 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 Nonassociative rings and algebras (17-XX)
16 Approximations and expansions (41-XX)
15 Abstract harmonic analysis (43-XX)
15 Systems theory; control (93-XX)
14 Global analysis, analysis on manifolds (58-XX)
13 Associative rings and algebras (16-XX)
13 Topological groups, Lie groups (22-XX)
12 Ordinary differential equations (34-XX)
12 Information and communication theory, circuits (94-XX)
10 Convex and discrete geometry (52-XX)
10 Fluid mechanics (76-XX)
9 Real functions (26-XX)
8 History and biography (01-XX)
7 Classical thermodynamics, heat transfer (80-XX)
6 Integral transforms, operational calculus (44-XX)
4 Difference and functional equations (39-XX)
4 Calculus of variations and optimal control; optimization (49-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 Mathematical logic and foundations (03-XX)
3 Field theory and polynomials (12-XX)
3 Sequences, series, summability (40-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 Algebraic topology (55-XX)
1 Mechanics of deformable solids (74-XX)
1 Geophysics (86-XX)
1 Mathematics education (97-XX)

Citations by Year

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