Coarse geometry and randomness. École d'Été de Probabilités de Saint-Flour XLI -- 2011 (Q390823): Difference between revisions
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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. | |||
| Property / 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. / rank | |||
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| Property / reviewed by | |||
| Property / reviewed by: Yilun Shang / rank | |||
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| Property / Mathematics Subject Classification ID | |||
| Property / Mathematics Subject Classification ID: 05-02 / rank | |||
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| Property / Mathematics Subject Classification ID: 05C10 / rank | |||
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| Property / Mathematics Subject Classification ID | |||
| Property / Mathematics Subject Classification ID: 05C80 / rank | |||
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| Property / Mathematics Subject Classification ID | |||
| Property / Mathematics Subject Classification ID: 05C81 / rank | |||
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| Property / Mathematics Subject Classification ID | |||
| Property / Mathematics Subject Classification ID: 82B41 / rank | |||
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| Property / Mathematics Subject Classification ID: 82B43 / rank | |||
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| Property / zbMATH DE Number | |||
| Property / zbMATH DE Number: 6243708 / rank | |||
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Revision as of 14:02, 29 June 2023
scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Coarse geometry and randomness. École d'Été de Probabilités de Saint-Flour XLI -- 2011 |
scientific article |
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Coarse geometry and randomness. École d'Été de Probabilités de Saint-Flour XLI -- 2011 (English)
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9 January 2014
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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.
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