Document Type

Report

Date

1999

Embargo Period

10-2011

Keywords

interacting partle systems, longtime behavior, clustering, recurrence, argodicity, mutually catalytic branching, branching

Language

English

Disciplines

Mathematics

Description/Abstract

Many interacting particle systems with short range interactions are not ergodic, but converge weakly towards a mixture of their ergodic invariant measures. The question arises whether a.s. the process eventually stays close to one of these ergodic states, or if it changes between the attainable ergodic states infinitely often ("recurrence"). Under the assumption that there exists a convergence--determining class of distributions that is (strongly) preserved under the dynamics, we show that the system is in fact recurrent in the above sense. We apply our method to several interacting particle systems, obtaining new or improved recurrence results. In addition, we answer a question raised by Ed Perkins concerning the change of the locally predominant type in a model of mutually catalytic branching.

Creative Commons License

Creative Commons Attribution 3.0 License
This work is licensed under a Creative Commons Attribution 3.0 License.

Included in

Mathematics Commons

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