Localisation in a growth model with interaction

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

doi:10.1007/s10955-018-2055-4

Localisation in a growth model with interaction

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

Authors

Marcelo Costa

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

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© The Author(s) 2018.
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