Critical percolation on any quasi-transitive graph of exponential growth has no infinite clusters
Accepted version
Peer-reviewed
Repository URI
Repository DOI
Change log
Authors
Hutchcroft, Tom
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.
Description
Keywords
math.PR, math.PR, math-ph, math.MP
Journal Title
Comptes Rendus Mathematique (Academie des Sciences)
Conference Name
Journal ISSN
0764-4442
1778-3569
1778-3569
Volume Title
354
Publisher
Elsevier