Localisation in a growth model with interaction
Probability
2018-05-23 v1
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 interactions. 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.
Cite
@article{arxiv.1711.07768,
title = {Localisation in a growth model with interaction},
author = {Marcelo Costa and Mikhail Menshikov and Vadim Shcherbakov and Marina Vachkovskaia},
journal= {arXiv preprint arXiv:1711.07768},
year = {2018}
}
Comments
31 pages, 2 figures