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Localisation in a growth model with interaction. Arbitrary graphs

Menshikov, Mikhail; Shcherbakov, Vadim

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Authors

Vadim Shcherbakov



Abstract

This paper concerns the long term behaviour of a growth model describing a random sequential allocation of particles on a finite graph. The probability of allocating a particle at a vertex is proportional to a log-linear function of numbers of existing particles in a neighbourhood of a vertex. When this function depends only on the number of particles in the vertex, the model becomes a special case of the generalised Pólya urn model. In this special case all but finitely many particles are allocated at a single random vertex almost surely. In our model interaction leads to the fact that, with probability one, all but finitely many particles are allocated at vertices of a maximal clique.

Citation

Menshikov, M., & Shcherbakov, V. (2020). Localisation in a growth model with interaction. Arbitrary graphs. Alea (2006. Online), 17(1), 473-489. https://doi.org/10.30757/alea.v17-19

Journal Article Type Article
Acceptance Date Apr 9, 2020
Publication Date 2020
Deposit Date Jun 17, 2020
Publicly Available Date Jun 17, 2020
Journal Alea (2006)
Electronic ISSN 1980-0436
Publisher Instituto Nacional de Matemática Pura e Aplicada
Peer Reviewed Peer Reviewed
Volume 17
Issue 1
Pages 473-489
DOI https://doi.org/10.30757/alea.v17-19
Public URL https://durham-repository.worktribe.com/output/1262550

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