Percolation beyond ℤd: The contributions of Oded Schramm

2011/09/01 by Olle Häggström
Mathematics · Physics and Astronomy · #Combinatorics #Field (mathematics) #Mathematical economics #Mathematics #Percolation (cognitive psychology) #Percolation theory #Physics #Pure mathematics #Random Matrices and Applications #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Topology (electrical circuits) #math.PR

paper · pdf · doi:10.1214/10-aop563

published as Annals of Probability 2011, Vol. 39, No. 5, 1668-1701 · 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)

openalex publication_date 2011/09/01 · arxiv created 2011/11/29 · arxiv updated 2011/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06

Abstract

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

Citations

• Random walk on the infinite cluster of the percolation model
• Choosing a Spanning Tree for the Integer Lattice Uniformly
• Quenched invariance principle for simple random walk on percolation clusters
• The critical probability for random Voronoi percolation in the plane is 1/2
• Generating random spanning trees more quickly than the cover time
• Ueber die Auflösung der Gleichungen, auf welche man bei der Untersuchung der linearen Vertheilung galvanischer Ströme geführt wird
• Scaling limits of loop-erased random walks and uniform spanning trees
• Quantitative noise sensitivity and exceptional times for percolation
• Visibility to infinity in the hyperbolic plane, despite obstacles
• Perplexing Problems in Probability
• Percolation
• Percolation