Localisation in a growth model with interaction

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

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