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The 1996 Wald memorial lectures. Stochastic models of interacting systems. (English) Zbl 0873.60072
These are popularized lectures by a leading probabilist in the field. The author reviews some personal experience and a brief history on the subject. Then, he goes to some typical models: stochastic Ising models, contact processes, voter models and exclusion processes. Some background, some recent exciting progress as well as some applications are addressed. The paper should be readable for a very large range of researchers, not only for probabilists. Certainly, as the author mentions, it becomes impossible today to survey the entire subject even in a book, he emphasizes the line developed in the States. For instance, except somehow more direct applications of IPS (interacting particle systems) to the applied areas, one may also mention a few words on the application of the coupling technique, original developed in the study on IPS, to the pure mathematics including Riemannian geometry.

MSC:
60K35 Interacting random processes; statistical mechanics type models; percolation theory
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[96] LOS ANGELES, CALIFORNIA 90095 E-MAIL: tml@math.ucla.edu
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