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A coupling of finite particle systems

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

T. S. Mountford
T. S. Mountford*
Affiliation:
University of California, Los Angeles
*
∗ Postal address: Department of Mathematics, University of California, Los Angeles, CA 90024, USA.
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Abstract

We show that for a large class of one-dimensional interacting particle systems, with a finite initial configuration, any limit measure , for a sequence of times tending to infinity, must be invariant. This result is used to show that the one-dimensional biased annihilating branching process with parameter > 1/3 converges in distribution to the upper invariant measure provided its initial configuration is almost surely finite and non-null.

Keywords

CONTINUOUS-TIME MARKOV CHAININTERACTING PARTICLE SYSTEMINVARIANT MEASURE

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Type
Short Communications
Information
Journal of Applied Probability , Volume 30 , Issue 1 , March 1993 , pp. 258 - 262
Copyright
Copyright © Applied Probability Trust 1993 

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Footnotes

Research partially supported by NSF Grant DMS-9157461 and the Sloan Foundation.

References

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