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Localisation in a growth model with interaction.

Costa, Marcelo and Menshikov, Mikhail and Shcherbakov, Vadim and Vachkovskaia, Marina (2018) 'Localisation in a growth model with interaction.', Journal of statistical physics., 171 (6). pp. 1150-1175.

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.

Item Type:Article
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1007/s10955-018-2055-4
Publisher statement:© The Author(s) 2018. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Date accepted:01 May 2018
Date deposited:03 May 2018
Date of first online publication:08 May 2018
Date first made open access:07 June 2018

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