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

Hutchcroft, Thomas

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Authors

Hutchcroft, Thomas

Publication Date

2016-09-01

Journal Title

Comptes Rendus Mathematique (Academie des Sciences)

ISSN

0764-4442

Publisher

Elsevier

Volume

354

Issue

Pages

944-947

Type

Article

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Citation

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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