## The Annals of Probability

### Rapid Convergence to Equilibrium in One Dimensional Stochastic Ising Models

Richard Holley

#### 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

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