Hauptseminar Geometrie

Consider any nonelementary action of a hyperbolic group G on a not necessarily proper Gromov hyperbolic space X. The action is not assumed to be discrete and X is not assumed to be proper. We prove certain asymptotic properties for the action, including the following.
1)With respect to the Patterson-Sullivan measure on the boundary of G, the image in X of almost every word-geodesic in G sublinearly tracks a geodesic in X.
2)The proportion of elements in a Cayley-ball of radius R in G which act loxodromically on X converges to 1 with R.

We do this by using Cannon's theorem that hyperbolic groups admit a bicombing, generalizing to Markov processes on groups analogous results of Maher-Tiozzo for random walks, and realizing the Patterson-Sullivan measure as a stationary measure for such a Markov process. I might also discuss applications to other Markov processes such as non-backtracking random walks and ideas for extending these methods beyond hyperbolic groups. This is based on ongoing work with Sam Taylor and Giulio Tiozzo.

Donnerstag, den 10. Dezember 2015 um 12:00 Uhr, in INF288, HS5 Donnerstag, den 10. Dezember 2015 at 12:00, in INF288, HS5

Der Vortrag folgt der Einladung von The lecture takes place at invitation by Professor Anna Wienhard