Random Walks, Brownian Motion, and Interacting Particle Systems
Random Walks, Brownian Motion, and Interacting Particle Systems

Author: H. Kesten

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 457

ISBN-13: 1461204593

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This collection of articles is dedicated to Frank Spitzer on the occasion of his 65th birthday. The articles, written by a group of his friends, colleagues, former students and coauthors, are intended to demonstrate the major influence Frank has had on probability theory for the last 30 years and most likely will have for many years to come. Frank has always liked new phenomena, clean formulations and elegant proofs. He has created or opened up several research areas and it is not surprising that many people are still working out the consequences of his inventions. By way of introduction we have reprinted some of Frank's seminal articles so that the reader can easily see for himself the point of origin for much of the research presented here. These articles of Frank's deal with properties of Brownian motion, fluctuation theory and potential theory for random walks, and, of course, interacting particle systems. The last area was started by Frank as part of the general resurgence of treating problems of statistical mechanics with rigorous probabilistic tools.

Particle Systems, Random Media and Large Deviations
Particle Systems, Random Media and Large Deviations

Author: Richard Durrett

Publisher: American Mathematical Soc.

Published: 1985

Total Pages: 394

ISBN-13: 0821850423

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Covers the proceedings of the 1984 AMS Summer Research Conference. This work provides a summary of results from some of the areas in probability theory; interacting particle systems, percolation, random media (bulk properties and hydrodynamics), the Ising model and large deviations.

Sojourns in Probability Theory and Statistical Physics - III
Sojourns in Probability Theory and Statistical Physics - III

Author: Vladas Sidoravicius

Publisher: Springer Nature

Published: 2019-10-17

Total Pages: 341

ISBN-13: 9811503028

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Charles M. (Chuck) Newman has been a leader in Probability Theory and Statistical Physics for nearly half a century. This three-volume set is a celebration of the far-reaching scientific impact of his work. It consists of articles by Chuck’s collaborators and colleagues across a number of the fields to which he has made contributions of fundamental significance. This publication was conceived during a conference in 2016 at NYU Shanghai that coincided with Chuck's 70th birthday. The sub-titles of the three volumes are: I. Spin Glasses and Statistical Mechanics II. Brownian Web and Percolation III. Interacting Particle Systems and Random Walks The articles in these volumes, which cover a wide spectrum of topics, will be especially useful for graduate students and researchers who seek initiation and inspiration in Probability Theory and Statistical Physics.

Genealogies Of Interacting Particle Systems
Genealogies Of Interacting Particle Systems

Author: Matthias Birkner

Publisher: World Scientific

Published: 2020-02-24

Total Pages: 363

ISBN-13: 9811206104

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Interacting particle systems are Markov processes involving infinitely many interacting components. Since their introduction in the 1970s, researchers have found many applications in statistical physics and population biology. Genealogies, which follow the origin of the state of a site backwards in time, play an important role in their studies, especially for the biologically motivated systems.The program Genealogies of Interacting Particle Systems held at the Institute for Mathematical Sciences, National University of Singapore, from 17 July to 18 Aug 2017, brought together experts and young researchers interested in this modern topic. Central to the program were learning sessions where lecturers presented work outside of their own research, as well as a normal workshop. This is reflected in the present volume which contains two types of articles:Written by respected researchers, including experts in the field such as Steve Evans, member of the US National Academy of Sciences, as well as Anton Wakolbinger, Andreas Greven, and many others, this volume will no doubt be a valuable contribution to the probability community.

Hydrodynamic Behavior and Interacting Particle Systems
Hydrodynamic Behavior and Interacting Particle Systems

Author: George Papanicolaou

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 215

ISBN-13: 1468463470

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This IMA Volume in Mathematics and its Applications HYDRODYNAMIC BEHAVIOR AND INTERACTING PARTICLE SYSTEMS is in part the proceedings of a workshop which was an integral part of the 1985-86 IMA program on STOCHASTIC DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS. We are grateful to the Scientific Committee: Daniel Stroock (Chairman) Wendell Fleming Theodore Harris Pierre-Louis Lions Steven Orey George Papanicolaou for planning and implementing an exciting and stimulating year-long program. We especially thank the Program Organizer, George Papanicolaou for orga nizing a workshop which brought together scientists and mathematicians in a variety of areas for a fruitful exchange of ideas. George R. Sell Hans Weinberger PREFACE A workshop on the hydrodynamic behavior of interacting particle systems was held at the Institute for Mathematics and its Applications at the University of Minnesota during the week of March 17, 1986. Fifteen papers presented at the workshop are collected in this volume. They contain research in several different directions that are currently being pursued. The paper of Chaikin, Dozier and Lindsay is concerned with experimental results on suspensions in regimes where modern mathematical methods could be useful. The paper of Fritz gives an introduction to these methods as does the paper of Spohn. Analytical methods currently used by in the physics and chemistry literature are presented in the paper of Freed, Wang and Douglas. The paper of Caflisch deals with time dependent effects in sedimentation.

Continuous Time Markov Processes
Continuous Time Markov Processes

Author: Thomas Milton Liggett

Publisher: American Mathematical Soc.

Published: 2010

Total Pages: 290

ISBN-13: 0821849492

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Markov processes are among the most important stochastic processes for both theory and applications. This book develops the general theory of these processes, and applies this theory to various special examples.

Random Walks, Random Fields, and Disordered Systems
Random Walks, Random Fields, and Disordered Systems

Author: Anton Bovier

Publisher: Springer

Published: 2015-09-21

Total Pages: 254

ISBN-13: 3319193392

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Focusing on the mathematics that lies at the intersection of probability theory, statistical physics, combinatorics and computer science, this volume collects together lecture notes on recent developments in the area. The common ground of these subjects is perhaps best described by the three terms in the title: Random Walks, Random Fields and Disordered Systems. The specific topics covered include a study of Branching Brownian Motion from the perspective of disordered (spin-glass) systems, a detailed analysis of weakly self-avoiding random walks in four spatial dimensions via methods of field theory and the renormalization group, a study of phase transitions in disordered discrete structures using a rigorous version of the cavity method, a survey of recent work on interacting polymers in the ballisticity regime and, finally, a treatise on two-dimensional loop-soup models and their connection to conformally invariant systems and the Gaussian Free Field. The notes are aimed at early graduate students with a modest background in probability and mathematical physics, although they could also be enjoyed by seasoned researchers interested in learning about recent advances in the above fields.

Phase Transitions Of Interacting Particle Systems
Phase Transitions Of Interacting Particle Systems

Author: Norio Konno

Publisher: World Scientific

Published: 1995-01-16

Total Pages: 245

ISBN-13: 9814501182

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Recently, interacting particle systems have been studied widely from the standpoints of mathematics, physics, chemistry and biology. Many researchers are becoming interested in this field.This book focuses on the phase transitions of interacting particle systems, especially their critical values and order parameters. It poses the following question: How can we get good bounds on the critical values and the order parameters? This question is very basic, and many researchers have been trying to get better bounds rigorously. Hence the book provides bounds — both the author's and others'.