Attracting random walks Article Swipe
Julia Gaudio
,
Yury Polyanskiy
·
YOU?
·
· 2020
· Open Access
·
· DOI: https://doi.org/10.1214/20-ejp471
YOU?
·
· 2020
· Open Access
·
· DOI: https://doi.org/10.1214/20-ejp471
This paper introduces the Attracting Random Walks model, which describes the dynamics of a system of particles on a graph with $n$ vertices. At each step, a single particle moves to an adjacent vertex (or stays at the current one) with probability proportional to the exponent of the number of other particles at a vertex. From an applied standpoint, the model captures the rich get richer phenomenon. We show that the Markov chain exhibits a phase transition in mixing time, as the parameter governing the attraction is varied. Namely, mixing time is $O(n\log n)$ when the temperature is sufficiently high and $\exp(Ω(n))$ when temperature is sufficiently low. When $\mathcal{G}$ is the complete graph, the model is a projection of the Potts model, whose mixing properties and the critical temperature have been known previously. However, for any other graph our model is non-reversible and does not seem to admit a simple Gibbsian description of a stationary distribution. Notably, we demonstrate existence of the dynamic phase transition without decomposing the stationary distribution into phases.
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- Type
- preprint
- Language
- en
- Landing Page
- https://doi.org/10.1214/20-ejp471
- OA Status
- gold
- References
- 8
- Related Works
- 19
- OpenAlex ID
- https://openalex.org/W2919987542
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https://openalex.org/W2919987542Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.1214/20-ejp471Digital Object Identifier
- Title
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Attracting random walksWork title
- Type
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preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
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2020Year of publication
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2020-01-01Full publication date if available
- Authors
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Julia Gaudio, Yury PolyanskiyList of authors in order
- Landing page
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https://doi.org/10.1214/20-ejp471Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
goldOpen access status per OpenAlex
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https://doi.org/10.1214/20-ejp471Direct OA link when available
- Concepts
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Statistical physics, Random walk, Stationary distribution, Markov chain, Vertex (graph theory), Mixing (physics), Mathematics, Potts model, Graph, Exponent, Omega, Combinatorics, Phase transition, Complete graph, Physics, Thermodynamics, Quantum mechanics, Ising model, Philosophy, Statistics, LinguisticsTop concepts (fields/topics) attached by OpenAlex
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0Total citation count in OpenAlex
- References (count)
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- Related works (count)
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19Other works algorithmically related by OpenAlex
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