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Time to Absorption for a Heterogeneous Neutral Competition Model

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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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Acknowledgments

AM acknowledges Cariparo foundation for financial support. We thank Miguel Muñoz for useful discussions, comments and suggestions.

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Authors and Affiliations

  1. DISAT, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 , Torino, Italy

    Claudio Borile

  2. Dipartimento di Matematica, Università di Padova, via Trieste 63, 35121, Padova, Italy

    Paolo Dai Pra & Markus Fischer

  3. Dipartimento di Fisica “G. Galilei”, Università di Padova, via Marzolo 8, 35151,  Padova, Italy

    Marco Formentin & Amos Maritan

Authors
  1. Claudio Borile
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  2. Paolo Dai Pra
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  3. Markus Fischer
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  4. Marco Formentin
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  5. Amos Maritan
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Correspondence to Marco Formentin.

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Borile, C., Pra, P.D., Fischer, M. et al. Time to Absorption for a Heterogeneous Neutral Competition Model. J Stat Phys 156, 119–130 (2014). https://doi.org/10.1007/s10955-014-0989-8

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  • DOI: https://doi.org/10.1007/s10955-014-0989-8

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