The Annals of Probability

Controlled Spin-Flip Systems

Lawrence Gray

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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

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

First available in Project Euclid: 19 April 2007

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Zentralblatt MATH identifier


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

Spin-flip process controlled spin-flip systems martingale problem


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

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