Publication details for Mikhail MenshikovCosta, Marcelo, Menshikov, Mikhail, Shcherbakov, Vadim & Vachkovskaia, Marina (2018). Localisation in a growth model with interaction. Journal of Statistical Physics 171(6): 1150-1175.
- Publication type: Journal Article
- ISSN/ISBN: 0022-4715, 1572-9613
- DOI: 10.1007/s10955-018-2055-4
- Further publication details on publisher web site
- Durham Research Online (DRO) - may include full text
Author(s) from Durham
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.