Is the critical percolation probability local?

By Itai Benjamini, Asaf Nachmias, Yuval Peres. 2009

92 citations recorded by the source corpus.

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.

Subfields: Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/5927657985710b338799002532ed8e24ee23a9a4

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

In Statistics and Probability

Citations in the corpus

A New Proof of the Sharpness of the Phase Transition for Bernoulli Percolation and the Ising Model (2015, background): “ontinuity(1.2)alsoholds for c (thisalsofollowedfrom[Ham57]andtheexponentialdecayin 4 subcritical,butthedeﬁnitionof~ c illustratesthispropertyreadily). Thelocalityconjecture,duetoSchrammandpresentedin[BNP11], statesthat forany ">0, the map G( c(G) should becontinuous onthesetofgraphswith c&lt”
Asymptotics of cover times via Gaussian free fields: Bounded-degree graphs and general trees (2011, methodology): “This type of perturbation method was used by Ajtai, Koml´os and Sze-mer´edi [2] in the study of percolation, and found its applications later in that area (see, e.g., [6, 8]).”
Probability on Trees and Networks (2017, methodology): “For other codings of the trees as random walks, as well as various uses, see Geiger (1995), Pitman (1998), Bennies and Kersting (2000), Dwass (1969), Harris (1952), Le Gall and Le Jan (1998), Duquesne and Le Gall (2002), Marckert and Mokkadem (2003), Marckert (2008), Lamperti (1967), and Kendall (19”