Celebratio Mathematica — Liggett — Complete Bibliography

Complete Bibliography

Works connected to Abraham Wald

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T. M. Liggett: “Stochastic models of interacting systems,” Ann. Probab. 25 : 1 (1997), pp. 1–29. From the 1996 Wald Memorial Lectures. MR 1428497 Zbl 0873.60072 article

Interacting particle systems is by now a mature area of probability theory, but one that is still very active. We begin this paper by explaining how models from this area arise in fields such as physics and biology. We turn then to a discussion of both older and more recent results about them, concentrating on contact processes, voter models, and exclusion processes. These processes are among the most studied in the field, and have the virtue of relative simplicity in their description, which permits us to address the fundamental issues about their behavior without dealing with the extra complications that models from specific areas of application would require.