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Critical percolation on any quasi-transitive graph of exponential growth has no infinite clusters

Hutchcroft, Tom (2016) Critical percolation on any quasi-transitive graph of exponential growth has no infinite clusters. Comptes Rendus Mathematique, 354 (9). pp. 944-947. ISSN 1631-073X. doi:10.1016/j.crma.2016.07.013. https://resolver.caltech.edu/CaltechAUTHORS:20210924-190635043

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Abstract

We prove that critical percolation on any quasi-transitive graph of exponential volume growth does not have a unique infinite cluster. This allows us to deduce from earlier results that critical percolation on any graph in this class does not have any infinite clusters. The result is new when the graph in question is either amenable or nonunimodular.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/j.crma.2016.07.013DOIArticle
https://arxiv.org/abs/1605.05301arXivDiscussion Paper
ORCID:
AuthorORCID
Hutchcroft, Tom0000-0003-0061-593X
Alternate Title:La percolation critique sur les graphes quasi-transitifs à croissance exponentielle ne possède pas de composante connexe infinie
Additional Information:© 2016 Académie des sciences. Published by Elsevier Masson SAS Under an Elsevier user license. Received 3 July 2016, Accepted 27 July 2016, Available online 8 August 2016. This work was supported by a Microsoft Research PhD Fellowship and was carried out while the author was an intern at Microsoft Research, Redmond. We thank Ander Holroyd, Gady Kozma, Russ Lyons, Asaf Nachmias, and Tianyi Zheng for helpful comments and suggestions. We also thank Hugo Duminil-Copin and Ben Wallace for the french translation of the title and abstract.
Funders:
Funding AgencyGrant Number
Microsoft ResearchUNSPECIFIED
Issue or Number:9
DOI:10.1016/j.crma.2016.07.013
Record Number:CaltechAUTHORS:20210924-190635043
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20210924-190635043
Official Citation:Tom Hutchcroft, Critical percolation on any quasi-transitive graph of exponential growth has no infinite clusters, Comptes Rendus Mathematique, Volume 354, Issue 9, 2016, Pages 944-947, ISSN 1631-073X, https://doi.org/10.1016/j.crma.2016.07.013.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:111027
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:28 Sep 2021 14:26
Last Modified:28 Sep 2021 14:26

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