## The Annals of Probability

- Ann. Probab.
- Volume 6, Number 6 (1978), 953-974.

### Controlled Spin-Flip Systems

#### Abstract

We introduce a new tool into the study of spin-flip processes, which we call controlled spin-flip systems. For each spin-flip process we define a related class of controlled spin-flip systems. Our main theorem states that bounds on the behavior of a spin-flip process can be obtained by studying the behavior of the related controlled spin-flip system. Since controlled spin-flip systems are in general easier to work with than regular spin-flip processes (they correspond to finite state space Markov processes), our main theorem has applications to some of the important problems concerning spin-flip processes. In particular, we discuss several applications to the uniqueness problem. These include proofs of some new results, as well as new proofs of earlier results.

#### Article information

**Source**

Ann. Probab., Volume 6, Number 6 (1978), 953-974.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aop/1176995386

**Digital Object Identifier**

doi:10.1214/aop/1176995386

**Mathematical Reviews number (MathSciNet)**

MR512413

**Zentralblatt MATH identifier**

0392.60084

**JSTOR**

links.jstor.org

**Subjects**

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

**Keywords**

Spin-flip process controlled spin-flip systems martingale problem

#### Citation

Gray, Lawrence. Controlled Spin-Flip Systems. Ann. Probab. 6 (1978), no. 6, 953--974. doi:10.1214/aop/1176995386. https://projecteuclid.org/euclid.aop/1176995386