Is the critical percolation probability local?

Mathematics – Probability

Scientific paper

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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.

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