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Percolation on Finite Cayley Graphs

Published online by Cambridge University Press:  07 June 2006

CHRISTOPHER MALON  and
IGOR PAK
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)
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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
Information
Combinatorics, Probability and Computing , Volume 15 , Issue 4 , July 2006 , pp. 571 - 588
Copyright
2006 Cambridge University Press

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