Published November 2021
| Accepted Version
Journal Article
Open
No Percolation at Criticality on Certain Groups of Intermediate Growth
- Creators
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Hermon, Jonathan
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Hutchcroft, Tom
Chicago
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Abstract
We prove that critical percolation has no infinite clusters almost surely on any unimodular quasi-transitive graph satisfying a return probability upper bound of the form p_n(v,v) ≤ exp[−Ω(n^γ)] for some γ > ½. The result is new in the case that the graph is of intermediate volume growth.
Additional Information
© The Author(s) 2020. Published by Oxford University Press. This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model). Received: 01 October 2018; Revision received: 06 September 2019; Accepted: 10 September 2019; Published: 06 December 2019. We thank Gidi Amir and Tianyi Zheng for sharing their expertise on groups of intermediate growth. This work was supported by Engineering and Physical Sciences Research Council (EPSRC) (EP/L018896/1 to J.H.).Attached Files
Accepted Version - 1809.11112.pdf
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Additional details
- Eprint ID
- 111029
- Resolver ID
- CaltechAUTHORS:20210924-202109319
- Engineering and Physical Sciences Research Council (EPSRC)
- EP/L018896/1
- Created
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2021-09-27Created from EPrint's datestamp field
- Updated
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2021-12-17Created from EPrint's last_modified field