Professor Mikhail Menshikov mikhail.menshikov@durham.ac.uk
Professor
Localisation in a growth model with interaction. Arbitrary graphs
Menshikov, Mikhail; Shcherbakov, Vadim
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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