The harmonic measure for random walks on cocompact Fuchsian groups
speaker: Giulio Tiozzo (University of Toronto)abstract: We consider random walks on groups of isometries of the hyperbolic plane, known as Fuchsian groups. It is well-known since Furstenberg that such random walks converge to the boundary at infinity, and the probability to reach a given subset of the boundary defines a hitting, or harmonic, measure on the circle. It has been a long-standing question whether this harmonic measure is absolutely continuous with respect to the Lebesgue measure. Conjecturally, this is never the case for random walks on cocompact, discrete groups. In the talk, based on joint work with Petr Kosenko, we settle the conjecture for nearest neighbour random walks on hyperelliptic groups. In fact, we show that the dimension of the harmonic measure for such walks is strictly less than one. This is also related to an inequality between entropy and drift.
timetable:
Wed 22 Feb, 15:00 - 16:00, Sala Conferenze Centro De Giorgi
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