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過去の記録 ～10/25｜次回の予定｜今後の予定 10/26～
| 開催情報 | 月曜日 15:30～17:00 数理科学研究科棟(駒場) 号室 |
|---|---|
| 担当者 | 松井 宏樹、木田 良才、河東 泰之 |
| セミナーURL | https://sites.google.com/view/hirokimatui/tokyo-seminar |
2026年11月16日(月)
15:30-17:00 数理科学研究科棟(駒場) 126号室
阪本 皓貴 氏 (東大数理)
Continuity results for random walks in hyperbolic percolation
阪本 皓貴 氏 (東大数理)
Continuity results for random walks in hyperbolic percolation
[ 講演概要 ]
Benjamini, Lyons, and Schramm proved that the simple random walk on the infinite cluster of supercritical Bernoulli percolation exhibits positive drift and entropy, provided the underlying graph is the Cayley graph of a non-amenable group. A natural question then arises: how do these asymptotic quantities vary with the percolation parameter? In this talk, I will provide some background on this topic and show that these quantities are continuous in the parameter when the group is Gromov hyperbolic. I will also discuss how this continuity contrasts with the conjectured behavior of the Hausdorff dimension of the limit set.
Benjamini, Lyons, and Schramm proved that the simple random walk on the infinite cluster of supercritical Bernoulli percolation exhibits positive drift and entropy, provided the underlying graph is the Cayley graph of a non-amenable group. A natural question then arises: how do these asymptotic quantities vary with the percolation parameter? In this talk, I will provide some background on this topic and show that these quantities are continuous in the parameter when the group is Gromov hyperbolic. I will also discuss how this continuity contrasts with the conjectured behavior of the Hausdorff dimension of the limit set.
