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

TL;DR

This paper reviews Oded Schramm's influential work on percolation theory beyond the standard lattice ${f Z}^d$, focusing on nonamenable lattices and expanding the understanding of percolation in more complex structures.

Contribution

It highlights Schramm's pioneering contributions to extending percolation theory to nonamenable lattices, a significant advancement in the field.

Findings

Schramm's work advanced understanding of percolation on nonamenable lattices

The review summarizes key results and methods introduced by Schramm

It emphasizes the impact of his contributions on the development of the theory

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.