The Annals of Probability
- Ann. Probab.
- Volume 26, Number 4 (1998), 1751-1780.
Finite approximations to the critical reversible nearest particle system
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.
Ann. Probab., Volume 26, Number 4 (1998), 1751-1780.
First available in Project Euclid: 31 May 2002
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 82C22: Interacting particle systems [See also 60K35]
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