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Operator Algebra Seminars
Seminar information archive ～10/25｜Next seminar｜Future seminars 10/26～
| Date, time & place | Monday 15:30 - 17:00 Room # (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | MATUI Hiroki, KIDA Yoshikata, KAWAHIGASHI Yasuyuki |
2026/11/16
15:30-17:00 Room # 126 (Graduate School of Math. Sci. Bldg.)
Kohki Sakamoto (The University of Tokyo)
Continuity results for random walks in hyperbolic percolation
Kohki Sakamoto (The University of Tokyo)
Continuity results for random walks in hyperbolic percolation
[ Abstract ]
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.
