Percolation on Hyperbolic Graphs
Published version
Peer-reviewed
Repository URI
Repository DOI
Change log
Authors
Hutchcroft, Thomas https://orcid.org/0000-0003-0061-593X
Abstract
We prove that Bernoulli bond percolation on any nonamenable, Gromov
hyperbolic, quasi-transitive graph has a phase in which there are infinitely
many infinite clusters, verifying a well-known conjecture of Benjamini and
Schramm (1996) under the additional assumption of hyperbolicity. In other
words, we show that
Description
Keywords
math.PR, math.PR, math-ph, math.MP
Journal Title
Geometric and Functional Analysis
Conference Name
Journal ISSN
1016-443X
1420-8970
1420-8970
Volume Title
29
Publisher
Springer Science and Business Media LLC
Publisher DOI
Sponsorship
Herchel Smith Fund