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arXiv · 1711.07768

Localisation in a growth model with interaction

Marcelo Costa·Mikhail Menshikov·Vadim Shcherbakov·Marina Vachkovskaia
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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.

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Marcelo Costa, Mikhail Menshikov, Vadim Shcherbakov, Marina Vachkovskaia. 2017-11-21. Localisation in a growth model with interaction. https://doi.org/10.1007/s10955-018-2055-4

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