Branching-coalescing particle systems |
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Authors: | Siva R?Arthreya Email author" target="_blank">Jan M?SwartEmail author |
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Institution: | (1) Indian Statistical Institute, 8th mile Mysore Road, RV College PO, Bangalore, -560059, India;(2) Mathematical Institute, University Erlangen-Nuremberg, Bismarckstraße 1 1/2, 91054 Erlangen, Germany |
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Abstract: | We study the ergodic behavior of systems of particles performing independent random walks, binary splitting, coalescence and deaths. Such particle systems are dual to systems of linearly interacting Wright-Fisher diffusions, used to model a population with resampling, selection and mutations. We use this duality to prove that the upper invariant measure of the particle system is the only homogeneous nontrivial invariant law and the limit started from any homogeneous nontrivial initial law.Mathematics Subject Classification (2000):Primary: 60K35, 92D25; Secondary: 60J80, 60J60Research supported in part by the German Science Foundation.AcknowledgementWe thank Klaus Fleischmann who played a stimulating role during the early stages of this project and answered a question about Laplace functionals, Claudia Neuhauser for answering questions about branching-coalescing processes, Olle Häggström for answering questions on nonamenable groups, and Tokuzo Shiga for answering our questions about his work. We thank the referee for drawing our attention to the reference SU86]. Part of this work was carried out during the visits of Siva Athreya to the Weierstrass Institute for Applied Analysis and Stochastics, Berlin and to the Friedrich-Alexander University Erlangen-Nuremberg, and of Jan Swart to the Indian Statistical Institute, Delhi. We thank all these places for their kind hospitality. |
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Keywords: | First Schlö gl Model Reaction-diffusion process Autocatalytic reaction Branching Coalescence Resampling Selection Mutation Contact process |
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