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October, 1977 On the Uniqueness and Nonuniqueness of Proximity Processes
Lawrence Gray, David Griffeath
Ann. Probab. 5(5): 678-692 (October, 1977). DOI: 10.1214/aop/1176995712


We discuss the uniqueness of a class of infinite particle systems known as proximity processes, with the aid of certain "dual" Markov chains. By checking whether the dual "explodes," i.e., attempts infinitely many jumps in a finite time, and how it explodes when it does, it is possible in many cases to determine whether or not there is more than one particle system with given flip rates. We then use duality to find an example of a system which is uniquely determined by its flip rates, but whose generator is not the closure of the naive operator formed from these flip rates.


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Lawrence Gray. David Griffeath. "On the Uniqueness and Nonuniqueness of Proximity Processes." Ann. Probab. 5 (5) 678 - 692, October, 1977.


Published: October, 1977
First available in Project Euclid: 19 April 2007

zbMATH: 0411.60099
MathSciNet: MR448629
Digital Object Identifier: 10.1214/aop/1176995712

Primary: 60K35

Keywords: Infinite particle system , Nonuniqueness , uniqueness

Rights: Copyright © 1977 Institute of Mathematical Statistics


Vol.5 • No. 5 • October, 1977
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