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Fixed price of groups and percolation

Published online by Cambridge University Press:  16 January 2012

RUSSELL LYONS
RUSSELL LYONS*
Affiliation:
Department of Mathematics, Indiana University, 831 E. 3rd St., Bloomington, IN 47405-7106, USA (email: rdlyons@indiana.edu)
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Abstract

We prove that for every finitely generated group Γ, at least one of the following holds: (1) Γ has fixed price; (2) each of its Cayley graphs G has infinitely many infinite clusters for some Bernoulli percolation on G.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 33 , Issue 1 , February 2013 , pp. 183 - 185
Copyright
Copyright © Cambridge University Press 2013

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