From the reviews "This book presents a complete treatment of a new class of random processes, which have been studied intensively during the last fifteen years. None of this material has ever appeared in book form before. The high quality of this work [...] makes a fascinating subject and its open problem as accessible as possible." Mathematical Reviews
Interacting Particle Systems (Classics in Mathematics)
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From the reviews: "This is a paperback reprint, in Springer’s Classics in Mathematics series, of a book originally published in 1985 in the Grundlehren series. … The reprint is well-made and easy to read. It will be welcomed by all specialists in the field." (Fernando Q. Gouvêa, MathDL, January, 2005) "The book enjoys its well-deserved reputation, it still gives a good overview of relevant models and a number of useful methods, it is clear and reliable … and deserves to be consulted by any serious researchers in mathematics or statistical physics who is interested in stochastic evolutions of many-particle (or many-spin) systems. … Springer’s decision to republish it as a "Classic in Mathematics’, making it available at an affordable price, thus is very welcome." (A. C. D. van Enter, Zentralblatt MATH, Vol. 1103 (5), 2007)
From the Back Cover
From the reviews "[...] This book presents a complete treatment of a new class of random processes, which have been studied intensively during the last fifteen years. None of this material has ever appeared in book form before. …The high quality of this work, on a technically difficult subject, makes a fascinating subject and its open problem as accessible as possible. [...]F.L. Spitzer in Mathematical Reviews, 1986 " [...] This book, the first monographic presentation of this important and rapidly developing theory, will prove indispensable to every serious student of stochastics [...]" S. Gacsályi in Publicationes Mathematicae, 1986 "[...] However, it can be said that the author has succeeded in what even experts are seldom able to achieve: To write a clearcut and inspiring book on his favorite subject which meets most, if not all requirements which can be imposed on a comprehensive text on an important new field. The author can be congratulated on his excellent presentation of the theory of interacting particle systems. The book is highly recommended to everyone who works on or is interested in this subject: to probabilists, physicists and theoretical biologists. [...]" G. Rosenkranz in Methods of Information in Medicine, 1986
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Inside This Book
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First Sentence:
The interacting particle systems which are the subject of this book are continuous-time Markov processes on certain spaces of configurations of particles. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
coalescing duality, symmetrized random walk, exclusion process corresponding, multitype voter model, particle system context, potlatch processes, symmetric exclusion process, upper invariant measure, extremal invariant measures, attractive spin systems, critical contact process, irreducible random walk, nonconstant bounded harmonic functions, exchangeable measures, finite range case, strictly positive rates, majority vote process, martingale problem, attractiveness assumption, reversible measures, translation invariant case, reggeon field theory, simple exclusion process, flip rates, renewal measure Key Phrases - Capitalized Phrases (CAPs): (learn more)
Some Basic, Dominated Convergence Theorem, Other General Results, Central Limit Theorem, Proof Let, Choquet-Deny Theorem, Proof Take, Bounded Convergence Theorem, Proof Suppose, Appendix of Nachbin, Finetti's Theorem, Krein-Milman Theorem, Proof By Theorem, Therefore Theorem, Van Doorn New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
The interacting particle systems which are the subject of this book are continuous-time Markov processes on certain spaces of configurations of particles. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
coalescing duality, symmetrized random walk, exclusion process corresponding, multitype voter model, particle system context, potlatch processes, symmetric exclusion process, upper invariant measure, extremal invariant measures, attractive spin systems, critical contact process, irreducible random walk, nonconstant bounded harmonic functions, exchangeable measures, finite range case, strictly positive rates, majority vote process, martingale problem, attractiveness assumption, reversible measures, translation invariant case, reggeon field theory, simple exclusion process, flip rates, renewal measure Key Phrases - Capitalized Phrases (CAPs): (learn more)
Some Basic, Dominated Convergence Theorem, Other General Results, Central Limit Theorem, Proof Let, Choquet-Deny Theorem, Proof Take, Bounded Convergence Theorem, Proof Suppose, Appendix of Nachbin, Finetti's Theorem, Krein-Milman Theorem, Proof By Theorem, Therefore Theorem, Van Doorn New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 26
books:
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100
books
cite this book:
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- Probability and Measure, 3rd Edition by Patrick Billingsley in Back Matter
- Gibbs States on Countable Sets (Cambridge Tracts in Mathematics) by Christopher J. Preston in Back Matter
- Theory of Phase Transitions (International series in natural philosophy) by Ya G. Sinai in Back Matter
- Additive and Cancellative Interacting Particle Systems (Lecture notes in mathematics ; 724) in Back Matter
- Branching Processes (Dover Books on Mathematics) by K. B. Athreya in Back Matter
See all 26 books this book cites
- Phase Transitions of Interacting Particle Systems by Norio Konno on 7 pages
- Nonequilibrium Statistical Mechanics in One Dimension (Cambridge Lecture Notes in Physics) by Vladimir Privman on 7 pages
- Progress in Probability by H. Kesten on 4 pages
- Topics in Contemporary Probability and Its Applications (Probability and Stochastics Series) by J. Laurie Snell on page 114, page 154, and page 230
- Mathematics and Computer Science III: Algorithms, Trees, Combinatorics and Probabilities (Trends in Mathematics) (v. 3) by Michael Drmota on page 413, and page 428
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