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Durham University

Department of Mathematical Sciences

Academic Staff

Publication details for Mikhail Menshikov

Costa, Marcelo, Menshikov, Mikhail, Shcherbakov, Vadim & Vachkovskaia, Marina (2018). Localisation in a growth model with interaction. Journal of Statistical Physics 171(6): 1150-1175.

Author(s) from Durham


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 interaction. 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.