The Annals of Probability

Finite approximations to the critical reversible nearest particle system

Thomas Mountford and Ted Sweet

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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

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

First available in Project Euclid: 31 May 2002

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Zentralblatt MATH identifier

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

Nearest particle system critical reversible spectral gap


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.

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