Hostname: page-component-7c8c6479df-fqc5m Total loading time: 0 Render date: 2024-03-29T11:15:45.795Z Has data issue: false hasContentIssue false

Percolation on Finite Cayley Graphs

Published online by Cambridge University Press:  07 June 2006

CHRISTOPHER MALON
Affiliation:
MIT Department of Mathematics, Cambridge, MA 02139, USA (e-mail: malon@math.mit.edu, pak@math.mit.edu)
IGOR PAK
Affiliation:
MIT Department of Mathematics, Cambridge, MA 02139, USA (e-mail: malon@math.mit.edu, pak@math.mit.edu)

Abstract

In this paper, we study percolation on finite Cayley graphs. A conjecture of Benjamini says that the critical percolation $p_c$ of any vertex-transitive graph satisfying a certain diameter condition can be bounded away from one. We prove Benjamini's conjecture for some special classes of Cayley graphs. We also establish a reduction theorem, which allows us to build Cayley graphs for large groups without increasing $p_c$.

Type
Paper
Copyright
2006 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)