Long Term Behaviour of Locally Interacting Birth-and-Death Processes

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Abstract

In this paper we study long-term evolution of a finite system of locally interacting birth-and-death processes labelled by vertices of a finite connected graph. A detailed description of the asymptotic behaviour is obtained in the case of both constant vertex degree graphs and star graphs. The model is motivated by modelling interactions between populations, adsorption-desorption processes and is related to interacting particle systems, Gibbs models with unbounded spins, as well as urn models with interaction.

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Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Probability Theory and Statistics

Keywords

  • Markov chain, Birth-and-death process, Gibbs measure, Reversibility, Recurrence, Transience, Explosion
Original languageEnglish
Pages (from-to)132-157
JournalJournal of Statistical Physics
Volume158
Issue number1
Publication statusPublished - 2015
Publication categoryResearch
Peer-reviewedYes