Percolation beyond ${\mathbb{Z}}^{\bolds{d}}$: The contributions of Oded Schramm

Abstract

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

Published in at http://dx.doi.org/10.1214/10-AOP563 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (3)

• Uniqueness and non-uniqueness in percolation theory
• Visibility to infinity in the hyperbolic plane, despite obstacles
• Percolation on nonunimodular transitive graphs

Cited by in corpus (3)

• Percolation on infinite graphs and isoperimetric inequalities
• Zero-temperature Glauber dynamics on the 3-regular tree and the median process
• Subcritical contact processes seen from a typical infected site