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.
Original language | English |
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Pages (from-to) | 1150-1175 |
Number of pages | 26 |
Journal | Journal of Statistical Physics |
Volume | 171 |
Early online date | 8 May 2018 |
DOIs | |
Publication status | Published - Jun 2018 |