Recurrence and ergodicity of interacting particle systems |
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Authors: | J Theodore Cox Achim Klenke |
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Institution: | Mathematics Department, Syracuse University, Syracuse, NY 13244, USA, US Mathematisches Institut, Universit?t Erlangen-Nürnberg, Bismarckstra?e 1?, 91054 Erlangen, Germany. e-mail: klenke@mi.uni-erlangen.de, DE
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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.
Received: 22 January 1999 / Revised version: 24 May 1999 |
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Keywords: | Mathematics Subject Classification (1991): Primary 60K35 |
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