Time to Absorption for a Heterogeneous Neutral Competition Model |
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Authors: | Claudio Borile Paolo Dai Pra Markus Fischer Marco Formentin Amos Maritan |
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Affiliation: | 1. DISAT, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129?, Torino, Italy 2. Dipartimento di Matematica, Università di Padova, via Trieste 63, 35121, Padova, Italy 3. Dipartimento di Fisica “G. Galilei”, Università di Padova, via Marzolo 8, 35151, ?Padova, Italy
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Abstract: | Neutral models aspire to explain biodiversity patterns in ecosystems where species difference can be neglected and perfect symmetry is assumed between species. Voter-like models capture the essential ingredients of the neutral hypothesis and represent a paradigm for other disciplines like social studies and chemical reactions. In a system where each individual can interact with all the other members of the community, the typical time to reach an absorbing state with a single species scales linearly with the community size. Here we show, by using a rigorous approach based on a large deviation principle and confirming previous approximate and numerical results, that in a mean-field heterogeneous voter model the typical time to reach an absorbing state scales exponentially with the system size. |
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