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Counterexamples for percolation on unimodular random graphs

Angel, Omer and Hutchcroft, Tom (2018) Counterexamples for percolation on unimodular random graphs. In: Unimodularity in randomly generated graphs. Contemporary Mathematics. No.719. American Mathematical Society , Providence, RI, pp. 11-28. ISBN 978-1-4704-3914-9. https://resolver.caltech.edu/CaltechAUTHORS:20210922-193309642

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Abstract

We construct an example of a bounded degree, nonamenable, unimodular random rooted graph with p_c = p_u for Bernoulli bond percolation, as well as an example of a bounded degree, unimodular random rooted graph with p_c < 1 but with an infinite cluster at criticality. These examples show that two well-known conjectures of Benjamini and Schramm are false when generalised from transitive graphs to unimodular random rooted graphs.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1090/conm/719/14465DOIArticle
https://arxiv.org/abs/1710.03003arXivDiscussion Paper
ORCID:
AuthorORCID
Angel, Omer0000-0002-6451-8242
Hutchcroft, Tom0000-0003-0061-593X
Additional Information:© 2018 Omer Angel and Thomas Hutchcroft. This was was carried out while TH was a PhD student at the University of British Columbia, during which time he was supported by a Microsoft Research PhD Fellowship.
Funders:
Funding AgencyGrant Number
Microsoft ResearchUNSPECIFIED
Subject Keywords:Unimodular random graphs, percolation, uniqueness, connectivity, nonamenable
Series Name:Contemporary Mathematics
Issue or Number:719
DOI:10.1090/conm/719/14465
Record Number:CaltechAUTHORS:20210922-193309642
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20210922-193309642
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:111008
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:27 Sep 2021 21:16
Last Modified:27 Sep 2021 21:16

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