Open Access
October 1998 Finite approximations to the critical reversible nearest particle system
Thomas Mountford, Ted Sweet
Ann. Probab. 26(4): 1751-1780 (October 1998). DOI: 10.1214/aop/1022855881


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.


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Thomas Mountford. Ted Sweet. "Finite approximations to the critical reversible nearest particle system." Ann. Probab. 26 (4) 1751 - 1780, October 1998.


Published: October 1998
First available in Project Euclid: 31 May 2002

zbMATH: 0966.82013
MathSciNet: MR1675071
Digital Object Identifier: 10.1214/aop/1022855881

Primary: 82C22

Keywords: critical , Nearest particle system , reversible , spectral gap

Rights: Copyright © 1998 Institute of Mathematical Statistics

Vol.26 • No. 4 • October 1998
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