The Annals of Probability
- Ann. Probab.
- Volume 13, Number 1 (1985), 72-89.
Rapid Convergence to Equilibrium in One Dimensional Stochastic Ising Models
Abstract
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.
Article information
Source
Ann. Probab., Volume 13, Number 1 (1985), 72-89.
Dates
First available in Project Euclid: 19 April 2007
Permanent link to this document
https://projecteuclid.org/euclid.aop/1176993067
Digital Object Identifier
doi:10.1214/aop/1176993067
Mathematical Reviews number (MathSciNet)
MR770629
Zentralblatt MATH identifier
0558.60077
JSTOR
links.jstor.org
Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 82A31
Keywords
Stochastic Ising model rate of convergence to equilibrium
Citation
Holley, Richard. Rapid Convergence to Equilibrium in One Dimensional Stochastic Ising Models. Ann. Probab. 13 (1985), no. 1, 72--89. doi:10.1214/aop/1176993067. https://projecteuclid.org/euclid.aop/1176993067
