The Annals of Probability

Finite approximations to the critical reversible nearest particle system

Thomas Mountford and Ted Sweet

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Abstract

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.

Article information

Source
Ann. Probab., Volume 26, Number 4 (1998), 1751-1780.

Dates
First available in Project Euclid: 31 May 2002

Permanent link to this document
https://projecteuclid.org/euclid.aop/1022855881

Digital Object Identifier
doi:10.1214/aop/1022855881

Mathematical Reviews number (MathSciNet)
MR1675071

Zentralblatt MATH identifier
0966.82013

Subjects
Primary: 82C22: Interacting particle systems [See also 60K35]

Keywords
Nearest particle system critical reversible spectral gap

Citation

Mountford, Thomas; Sweet, Ted. Finite approximations to the critical reversible nearest particle system. Ann. Probab. 26 (1998), no. 4, 1751--1780. doi:10.1214/aop/1022855881. https://projecteuclid.org/euclid.aop/1022855881


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