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Localisation in a growth model with interaction

Costa, Marcelo; Menshikov, Mikhail; Shcherbakov, Vadim; Vachkovskaia, Marina

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Marcelo Costa

Vadim Shcherbakov

Marina Vachkovskaia


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.


Costa, M., Menshikov, M., Shcherbakov, V., & Vachkovskaia, M. (2018). Localisation in a growth model with interaction. Journal of Statistical Physics, 171(6), 1150-1175.

Journal Article Type Article
Acceptance Date May 1, 2018
Online Publication Date May 8, 2018
Publication Date Jun 1, 2018
Deposit Date May 3, 2018
Publicly Available Date May 3, 2018
Journal Journal of Statistical Physics
Print ISSN 0022-4715
Electronic ISSN 1572-9613
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 171
Issue 6
Pages 1150-1175


Accepted Journal Article (296 Kb)

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Copyright Statement
© The Author(s) 2018.<br /> 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.

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