Finite approximations to the critical reversible nearest particle system

• 成果类型: Article
• 署名作者: Mountford, T; Sweet, T
• 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: 1998
• 页码: 1751-1780
• 关键词: convergence

摘要

Approximating a critical attractive reversible nearest particle system on a finite set from above is not difficult, but approximating it from below is less trivial, as the empty configuration is invariant. We develop a finite state Markov chain that deals with this issue. The rate of convergence for this chain is discovered through a mixing inequality in Jerrum and Sinclair; an application of that spectral gap bound in this case requires the use of randomized paths from state to state. For applications, we prove distributional results for semiinfinite and infinite critical RNPS.