Open Access
February, 1985 Rapid Convergence to Equilibrium in One Dimensional Stochastic Ising Models
Richard Holley
Ann. Probab. 13(1): 72-89 (February, 1985). DOI: 10.1214/aop/1176993067


We consider one dimensional stochastic Ising models with finite range interactions. For such processes we first prove that the semi-group of the process converges exponentially fast on the $L^2$ space of the Gibbs states. Under the additional hypothesis that the flip rates are attractive, we prove that the semigroup acting on the cylinder functions converges to equilibrium exponentially fast in the uniform norm.


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Richard Holley. "Rapid Convergence to Equilibrium in One Dimensional Stochastic Ising Models." Ann. Probab. 13 (1) 72 - 89, February, 1985.


Published: February, 1985
First available in Project Euclid: 19 April 2007

zbMATH: 0558.60077
MathSciNet: MR770629
Digital Object Identifier: 10.1214/aop/1176993067

Primary: 60K35
Secondary: 82A31

Keywords: Rate of convergence to equilibrium , stochastic Ising model

Rights: Copyright © 1985 Institute of Mathematical Statistics

Vol.13 • No. 1 • February, 1985
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