Interacting Particle Systems

by Thomas M. Liggett

Overview

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

Product Details

ISBN-13:	9783540226178
Publisher:	Springer Berlin Heidelberg
Publication date:	12/22/2004
Series:	Classics in Mathematics
Edition description:	Reprint of the 1st ed. Berlin Heidelberg New York 1985
Pages:	496
Product dimensions:	6.10(w) x 9.25(h) x (d)

About the Author

Thomas Liggett was born on March 29, 1944 in Danville, Kentucky. At the age of two, he moved with his missionary parents to Latin America. His early education took place primarily in Buenos Aires, Argentina and San Juan, Puerto Rico. He attended college at Oberlin, where he became interested in probability theory under the influence of Samuel Goldberg, who had been a student of William Feller. He continued his study of probability at Stanford, taking many classes with Kai Lai Chung, and writing a thesis on problems related to the invariance principle with Samuel Karlin. In 1969 he joined the UCLA faculty; he has spent his entire career there. In addition to his teaching and research activities, he has been active in academic administration, serving as vice-chair and chair of the UCLA Department of Mathematics.

Liggett was chief editor of The Annals of Probability in 1985-87. He was a Sloan and a Guggenheim Fellow, spoke at the the 1986 International Congress of Mathematicians, and was the 1996 Wald Memorial Lecturer for the Institute of Mathematical Statistics.

Professor Liggett's interest in interacting particle systems began shortly after his move to UCLA, when he read a preprint of Frank Spitzer's fundamental 1970 paper. It is an unusual paper, in that it is much more concerned with descriptions of models and statements of open problems than with proofs of theorems. It provided an ideal way for a young probabilist to test his mettle: The challenge was to solve as many of Spitzer's problems as he could. The subject of interacting particle systems has continued to be the main focus of his research. He has written two books (the other is

Stochastic Interacting Systems: Contact, Voter and Exclusion Processes) and over 60 papers in this area. He has also contributed to a number of other fields, including nonlinear semigroups, subadditive ergodic theory, negative dependence, optimal stopping, combinatorics, random graphs, and renewal theory.

Table of Contents

The Construction, and Other General Results.- Some Basic Tools.- Spin Systems.- Shastic Ising Models.- The Voter Model.- The Contact Process.- Nearest-Particle Systems.- The Exclusion Process.- Linear Systems with Values in [0,—)s.

Editorial Reviews

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 shastic 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 Publisher