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東京確率論セミナー
過去の記録 ～10/09｜次回の予定｜今後の予定 10/10～
| 開催情報 | 月曜日 16:00～17:30 数理科学研究科棟(駒場) 122号室 |
|---|---|
| 担当者 | 佐々田槙子、中島秀太（慶應義塾大学）、星野壮登（東京科学大学）、蛯名真久（東京科学大学） |
| セミナーURL | https://sites.google.com/view/tokyo-probability-seminar23/ |
2026年10月19日(月)
16:00-17:30 数理科学研究科棟(駒場) 122号室
15:20〜 ２階のコモンルームでTea timeを行います。ぜひこちらにもご参加ください。
阪本 皓貴 氏 (東京大学)
Singularity of harmonic measure on Poisson-Voronoi tessellations in hyperbolic spaces
15:20〜 ２階のコモンルームでTea timeを行います。ぜひこちらにもご参加ください。
阪本 皓貴 氏 (東京大学)
Singularity of harmonic measure on Poisson-Voronoi tessellations in hyperbolic spaces
[ 講演概要 ]
Poisson-Voronoi tessellations provide natural examples of invariant random tilings of homogeneous spaces. Benjamini, Paquette, and Pfeffer proved that the nearest-neighbor random walk on the Poisson-Voronoi tessellation of the hyperbolic plane has positive drift and hence converges to the boundary circle. They further conjectured that its hitting measure on the boundary is singular with respect to Lebesgue measure. I will explain how this follows from an ergodic-theoretic argument based on rerooting relations, and briefly discuss the higher-dimensional case as well.
Poisson-Voronoi tessellations provide natural examples of invariant random tilings of homogeneous spaces. Benjamini, Paquette, and Pfeffer proved that the nearest-neighbor random walk on the Poisson-Voronoi tessellation of the hyperbolic plane has positive drift and hence converges to the boundary circle. They further conjectured that its hitting measure on the boundary is singular with respect to Lebesgue measure. I will explain how this follows from an ergodic-theoretic argument based on rerooting relations, and briefly discuss the higher-dimensional case as well.
