seminar: Mean-proximal group actions
speaker: Alexey Osipov (Centro di Ricerca Matematica Ennio De Giorgi)abstract: We will start from consideration of a random walk on a countable finitely generated group G. A random walk can either be recurrent or transient. In case of transiense it is natural to pose a question about the space of different ways of reaching infinity. Probably the most natural way of defining such space is as a compactification of G such that a.e. trajectory of the random walk converges to some point of the compactification. We will study a mu-boundary, another (weaker) way of defining such space, via a so called mean-proximal action of G. We will give relevant definitions and consider the most important examples. It turnes out that if a group G has a normal hyperbolic subgroup H, then the corresponding action of a group G on the standard hyperbolic boundary of H is mean-proximal (i.e. the hyperbolic boundary of H is a mu-boundary for G). This result is, in essense, a generalization of an earlier result about mu-boundaries of normal extensions of free groups obtained by A.V. Malyutin and A.M. Vershik. If time permits, we will discuss some other results in this direction. The talk is based on a joint work with A.V. Malyutin.
timetable:
Tue 4 Dec, 14:00 - 15:00, Sala Conferenze Centro De Giorgi
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