Work

Localisation in a Growth Model with Interaction

Year: 2018

Type: article

Abstract: 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.

Source: Journal of Statistical Physics

DOI: 10.1007/s10955-018-2055-4

Authors: M. Costa, M. Menshikov, V. Shcherbakov, M. Vachkovskaia

Institutions: Durham University, Royal Holloway University of London, Universidade Estadual de Campinas (UNICAMP)

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: London Mathematical Society, Conselho Nacional de Desenvolvimento Científico e Tecnológico