Localisation in a Growth Model with Interaction

Marcelo Costa , Mikhail Menshikov, Vadim Shcherbakov, Marina Vachkovskaia

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This paper concerns the long term behaviour of a growth model describing a random sequential allocation of particles on a finite cycle graph. The model can be regarded as a reinforced urn model with graph-based interactions. It is motivated by cooperative sequential adsorption, where adsorption rates at a site depend on the configuration of existing particles in the neighbourhood of that site. Our main result is that, with probability one, the growth process will eventually localise either at a single site, or at a pair of neighbouring sites.
Original languageEnglish
Pages (from-to)1150-1175
Number of pages26
JournalJournal of Statistical Physics
Early online date8 May 2018
Publication statusPublished - Jun 2018

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