The 1996 Wald Memorial Lectures - Stochastic models of interacting systems

• 成果类型: Article
• 署名作者: Liggett, TM
• 署名单位: University of California System; University of California Los Angeles
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 1997
• 页码: 1-29
• 关键词: asymmetric simple exclusion; dimensional contact-processes; valued markov-processes; threshold voter models; LIMIT-THEOREMS; ising-models; sobolev inequalities; random-environments; shock fluctuations; ergodic theorems

摘要

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.