Is the critical percolation probability local?

Benjamini, Itai; Nachmias, Asaf; Peres, Yuval

Is the critical percolation probability local?

Authors

Benjamini, Itai

Nachmias, Asaf

Peres, Yuval

Description

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.
9 pages