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On Recurrence of Random Walks on Groups driven by a symmetric Gibbs measure

Hold Date 2012-06-15 14:00~2012-06-15 17:00

Place Seminar Room 3, Faculty of Mathematics building, Ito Campus

Object person  

Speaker Johannes Jaerisch (Osaka University)

We employ the Thermodynamic Formalism to investigate the skew product dynamics
given by a Markov shift whose symbols act on a countable group by multiplication.
We show that each recurrent symmetric Hölder continuous potential on the Markov shift
carries full topological pressure with respect to the skew product dynamics.
In particular, we obtain in this case, that the group is amenable, and that
the associated conservative eigenmeasure of the Ruelle-Perron-Frobenius operator
is a product measure.