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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.


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
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Publisher statement:© The Author(s) 2018. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, 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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