Mathematics – Probability
Scientific paper
2009-01-29
Mathematics
Probability
9 pages
Scientific paper
We show that the critical probability for percolation on a d-regular
non-amenable graph of large girth is close to the critical probability for
percolation on an infinite d-regular tree. This is a special case of a
conjecture due to O. Schramm on the locality of p_c. We also prove a finite
analogue of the conjecture for expander graphs.
Benjamini Itai
Nachmias Asaf
Peres Yuval
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