The 1996 Wald memorial lectures. Stochastic models of interacting systems. (English) Zbl 0873.60072

Liggett, Thomas M.

Ann. Probab. 25, No. 1, 1-29 (1997).

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.

Reviewer: Chen Mu-fa (Beijing)

MSC:

60K35

Interacting random processes; statistical mechanics type models; percolation theory

Keywords:

stochastic Ising model; contact processes; voter models; exclusion processes

References:

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