Marcelo Costa
Localisation in a growth model with interaction
Costa, Marcelo; Menshikov, Mikhail; Shcherbakov, Vadim; Vachkovskaia, Marina
Authors
Professor Mikhail Menshikov mikhail.menshikov@durham.ac.uk
Professor
Vadim Shcherbakov
Marina Vachkovskaia
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.
Citation
Costa, M., Menshikov, M., Shcherbakov, V., & Vachkovskaia, M. (2018). Localisation in a growth model with interaction. Journal of Statistical Physics, 171(6), 1150-1175. https://doi.org/10.1007/s10955-018-2055-4
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 |
DOI | https://doi.org/10.1007/s10955-018-2055-4 |
Public URL | https://durham-repository.worktribe.com/output/1359603 |
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Copyright 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.
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