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Percolation beyond Z<sup>d</sup>: The contributions of Oded Schramm

Journal article
Authors Olle Häggström
Published in Annals of Probability
Volume 39
Issue 5
Pages 1668-1701
ISSN 0091-1798
Publication year 2011
Published at Department of Mathematical Sciences, Mathematical Statistics
Pages 1668-1701
Language en
Links dx.doi.org/10.1214/10-aop563
https://gup.ub.gu.se/file/66306
Keywords Percolation, amenability, hyperbolic plane, mass transport, uniform, spanning forest, uniform spanning-trees, brownian intersection exponents, infinite, clusters, random-walks, invariant percolation, uniqueness threshold, critical probability, plane exponents, cayley-graphs, forests
Subject categories Mathematical statistics

Abstract

Oded Schramm (1961-2008) influenced greatly the development of percolation theory beyond the usual Z(d) setting; in particular, the case of nonamenable lattices. Here, we review some of his work in this field.

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