Critical percolation on any quasi-transitive graph of exponential growth has no infinite clusters
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Authors
Publication Date
2016-09-01Journal Title
Comptes Rendus Mathematique (Academie des Sciences)
ISSN
0764-4442
Publisher
Elsevier
Volume
354
Issue
9
Pages
944-947
Type
Article
Metadata
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Hutchcroft, T. (2016). Critical percolation on any quasi-transitive graph of exponential growth
has no infinite clusters. Comptes Rendus Mathematique (Academie des Sciences), 354 (9), 944-947. https://doi.org/10.1016/j.crma.2016.07.013
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.
Identifiers
External DOI: https://doi.org/10.1016/j.crma.2016.07.013
This record's URL: https://www.repository.cam.ac.uk/handle/1810/283543
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