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An infinite particle system with additive interactions

Published online by Cambridge University Press:  01 July 2016

Richard Durrett
Richard Durrett*
Affiliation:
University of California, Los Angeles
*
∗Postal address: Department of Mathematics, University of California, Los Angeles CA 90024, U.S.A.
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Abstract

The models under consideration are a class of infinite particle systems which can be written as a superposition of branching random walks. This paper gives some results about the limiting behavior of the number of particles in a compact set as t → ∞ and also gives both sufficient and necessary conditions for the existence of a non-trivial translation-invariant stationary distribution.

Keywords

INFINITE PARTICLE SYSTEMRANDOM WALKBRANCHING PROCESSPOINT PROCESS
Type
Research Article
Information
Advances in Applied Probability , Volume 11 , Issue 2 , June 1979 , pp. 355 - 383
Copyright
Copyright © Applied Probability Trust 1979 

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