Coarse geometry and randomness. École d'Été de Probabilités de Saint-Flour XLI -- 2011
type: Item
instance of: scholarly article
title: Coarse geometry and randomness. École d'Été de Probabilités de Saint-Flour XLI -- 2011
zbMATH Open document ID: 1282.05001
DOI: 10.1007/978-3-319-02576-6
author: Itai Benjamini
published in: Lecture Notes in Mathematics
publication date: 2014-01-09T00:00:00Z
review text: The lecture notes contained in the book provide a bird's eye view of recent advances in coarse geometry and randomness. The first part focuses on the infinite vertex transitive graphs, expander graphs, and hyperbolic graphs. Then many important concepts regarding percolation on graphs and random walks are introduced. In particular, local and scaling limits of graphs, critical percolation clusters, and percolation on expanders are dealt with. The Kaimanovich-Vershik entropic criterion for the existence of harmonic functions on Cayley graphs is presented. Some conjectures regarding the question ``Does non-amenability imply non-Liouville (i.e., it admits non-constant bounded harmonic functions) for general bounded degree graphs?'' are also discussed.
reviewed by: Yilun Shang
Mathematics Subject Classification ID: 05-02
Mathematics Subject Classification ID: 05C10
Mathematics Subject Classification ID: 05C80
Mathematics Subject Classification ID: 05C81
Mathematics Subject Classification ID: 82B41
Mathematics Subject Classification ID: 82B43
zbMATH DE Number: 6243708
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-3-319-02576-6
OpenAlex ID: W594205391
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description: scientific article; zbMATH DE number 6243708