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Interacting particle systems. With a new postface. Reprint of the 1985 edition. (English) Zbl 1103.82016
Classics in Mathematics. New York, NY: Springer (ISBN 3-540-22617-6/pbk). xv, 496 p. (2005).
Liggett’s “Interacting Particle Systems” to a certain extent defined the field when it came out, and part of its success is that by now the descriptions of earlier reviewers as “complete” or “comprehensive”, do not apply anymore. Still 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, with a rather analytic slant, and deserves to be consulted by any serious researcher in mathematics or statistical physics who is interested in stochastic evolutions of many-particle (or many-spin) systems. The present edition is supplemented by a short afterword in which a number of advances on the open problems of the original edition are discussed. Springer’s decision to republish it as a “Classic in Mathematics”, making it available at an affordable price, thus is very welcome.

82C22 Interacting particle systems in time-dependent statistical mechanics
82-02 Research exposition (monographs, survey articles) pertaining to statistical mechanics
60K35 Interacting random processes; statistical mechanics type models; percolation theory
60Jxx Markov processes
60-02 Research exposition (monographs, survey articles) pertaining to probability theory