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Central limit theorems for random walks on groups via Lipschitz harmonic functions

Michael Bjorklund
ETH

Ergodic Theory and Dynamical Systems

Organisers: Andrew Ferguson, Thomas Jordan

ABSTRACT
In this talk, the term "random walk" (or "measured group") will be reserved for
a countable group G together with a probability measure p on G whose support
is assumed to generate G. By a "limit theorem", we shall mean an asymptotic
statement about the convolution powers of p; the aim of this talk is to discuss
the utility of Lipschitz (linear growth) harmonic functions on (G,p) when investigating
limit theorems for random walks and how some ideas from non-commutative
geometry (spectral triples, correspondences etc.) turn out to be useful when
constructing such functions. We shall then apply the techniques to prove
central limit theorems for random walks on (sub-direct) products of Gromov
hyperbolic groups.