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A Note on the Spectral Gap of the Fredrickson–Andersen One Spin Facilitated Model
This note discusses the spectral gap of the Fredrickson–Andersen one spin facilitated model in two different settings. The model describes an interacting particle system on a graph, where each site is either occupied or empty; and a site may change its occupation when at least one of its neighbors i...
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Formato: | Online Artículo Texto |
Lenguaje: | English |
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Springer US
2020
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Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7683486/ https://www.ncbi.nlm.nih.gov/pubmed/33268908 http://dx.doi.org/10.1007/s10955-020-02666-1 |
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author | Shapira, Assaf |
author_facet | Shapira, Assaf |
author_sort | Shapira, Assaf |
collection | PubMed |
description | This note discusses the spectral gap of the Fredrickson–Andersen one spin facilitated model in two different settings. The model describes an interacting particle system on a graph, where each site is either occupied or empty; and a site may change its occupation when at least one of its neighbors is empty. We will first consider the model on the infinite lattice [Formula: see text] , with density close to 1. The second result is on finite graphs, with density that grows with the size of the graph in a way that guarantees O(1) empty sites. In both models lower and upper bounds on the spectral gap were known, but in general did not match. The purpose of this paper is to present new upper bounds that have the same asymptotics as the known lower bounds. |
format | Online Article Text |
id | pubmed-7683486 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2020 |
publisher | Springer US |
record_format | MEDLINE/PubMed |
spelling | pubmed-76834862020-11-30 A Note on the Spectral Gap of the Fredrickson–Andersen One Spin Facilitated Model Shapira, Assaf J Stat Phys Article This note discusses the spectral gap of the Fredrickson–Andersen one spin facilitated model in two different settings. The model describes an interacting particle system on a graph, where each site is either occupied or empty; and a site may change its occupation when at least one of its neighbors is empty. We will first consider the model on the infinite lattice [Formula: see text] , with density close to 1. The second result is on finite graphs, with density that grows with the size of the graph in a way that guarantees O(1) empty sites. In both models lower and upper bounds on the spectral gap were known, but in general did not match. The purpose of this paper is to present new upper bounds that have the same asymptotics as the known lower bounds. Springer US 2020-11-04 2020 /pmc/articles/PMC7683486/ /pubmed/33268908 http://dx.doi.org/10.1007/s10955-020-02666-1 Text en © The Author(s) 2020 Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
spellingShingle | Article Shapira, Assaf A Note on the Spectral Gap of the Fredrickson–Andersen One Spin Facilitated Model |
title | A Note on the Spectral Gap of the Fredrickson–Andersen One Spin Facilitated Model |
title_full | A Note on the Spectral Gap of the Fredrickson–Andersen One Spin Facilitated Model |
title_fullStr | A Note on the Spectral Gap of the Fredrickson–Andersen One Spin Facilitated Model |
title_full_unstemmed | A Note on the Spectral Gap of the Fredrickson–Andersen One Spin Facilitated Model |
title_short | A Note on the Spectral Gap of the Fredrickson–Andersen One Spin Facilitated Model |
title_sort | note on the spectral gap of the fredrickson–andersen one spin facilitated model |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7683486/ https://www.ncbi.nlm.nih.gov/pubmed/33268908 http://dx.doi.org/10.1007/s10955-020-02666-1 |
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