Texas A&M University, Department of
Mathematics, 216 Milner Hall, 3rd of March 2004, 3:00-4:00
Groups and Dynamcs Seminar
Convergence of
spherical averages for actions of free groups
Alexander Bufetov of Princeton
University and The Independent University of Moscow
One can naturally assign a class of stationary Markov processes to a
measure-preserving action of a free group. If the action of the
subgroup of squares is ergodic, then the powers of the corresponding
Markov operators converge almost everywhere. This approach allows us to
obtain convergence of weighted spherical averages for actions of free
groups and to generalize ergodic theorems by Grigorchuk as well as by
Nevo and Stein for actions of free groups.