2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/217802We 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 pagesProbabilityGroup Theorytext