Interacting Particle Systems: 276 (Grundlehren der Mathematischen Wissenschaften) - Hardcover

Liggett, Thomas M.

Hardcover

ISBN 10: 0387960694 ISBN 13: 9780387960692

Publisher: Springer-Verlag New York Inc., 1985

Synopsis

At what point in the development of a new field should a book be written about it? This question is seldom easy to answer. In the case of interacting particle systems, important progress continues to be made at a substantial pace. A number of problems which are nearly as old as the subject itself remain open, and new problem areas continue to arise and develop. Thus one might argue that the time is not yet ripe for a book on this subject. On the other hand, this field is now about fifteen years old. Many important of several basic models is problems have been solved and the analysis almost complete. The papers written on this subject number in the hundreds. It has become increasingly difficult for newcomers to master the proliferating literature, and for workers in allied areas to make effective use of it. Thus I have concluded that this is an appropriate time to pause and take stock of the progress made to date. It is my hope that this book will not only provide a useful account of much of this progress, but that it will also help stimulate the future vigorous development of this field.

About this title

Review

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)

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.

Edition details

• Publisher: Springer-Verlag New York Inc.
• Publication date: 1985
• Language: English
• ISBN 10: 0387960694
• ISBN 13: 9780387960692
• Binding: Hardcover
• Number of pages: 501