Localisation in a Growth Model with Interaction

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...

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Bibliographic Details
Published in:Journal of statistical physics 2018-06, Vol.171 (6), p.1150-1175
Main Authors: Costa, M., Menshikov, M., Shcherbakov, V., Vachkovskaia, M.
Format: Article
Language:English
Subjects:
ADSORPTION
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
CONFIGURATION
COOPERATIVES
GRAPH THEORY
Growth models
INTERACTIONS
Localization
Mathematical and Computational Physics
Physical Chemistry
Physics
Physics and Astronomy
PROBABILITY
Quantum Physics
RANDOMNESS
SIMULATION
Statistical Physics and Dynamical Systems
Theoretical
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Summary: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.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-018-2055-4