Is the critical percolation probability local?

Itai Benjamini; Asaf Nachmias; Yuval Peres

doi:10.1007/s00440-009-0251-5

Is the critical percolation probability local?

Itai Benjamini^*, Asaf Nachmias, Yuval Peres

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

40 Scopus citations

Abstract

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. We also prove a finite analogue of this statement, Valid for expander graphs, Without any girth assumption.

Original language	English
Pages (from-to)	261-269
Number of pages	9
Journal	Probability Theory and Related Fields
Volume	149
Issue number	1
DOIs	https://doi.org/10.1007/s00440-009-0251-5
State	Published - Mar 2011
Externally published	Yes

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10.1007/s00440-009-0251-5

Cite this

@article{9bb2faf255cf44219a652793d88c20a6,

title = "Is the critical percolation probability local?",

abstract = "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. We also prove a finite analogue of this statement, Valid for expander graphs, Without any girth assumption.",

author = "Itai Benjamini and Asaf Nachmias and Yuval Peres",

year = "2011",

month = mar,

doi = "10.1007/s00440-009-0251-5",

language = "אנגלית",

volume = "149",

pages = "261--269",

journal = "Probability Theory and Related Fields",

issn = "0178-8051",