Document Type
Report
Date
1999
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.
Recommended Citation
Cox, J. Theodore and Klenke, Achim, "Recurrence and Ergodicity of Interacting Particle Systems" (1999). Mathematics - All Scholarship. 6.
https://surface.syr.edu/mat/6
Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.
