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

Vadim Shcherbakov, Stanislav Volkov

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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.
Original languageEnglish
Pages (from-to)132-157
Number of pages26
JournalJournal of Statistical Physics
Issue number1
Early online date26 Sept 2014
Publication statusPublished - Jan 2015

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