Cesaro limit and ergodicity of locally eventually periodic measures

Speaker: Felipe Garcia-ramos

Date: Tue, Jun 19, 2012

Location: PIMS, University of British Columbia

Conference: PIMS-MPrime Summer School in Probability

Subject: Mathematics, Probability

Class: Scientific


We study translation invariant deterministic dynamics (phi) on the lattice (cellular automata). In particular the evolution and limit of probability measures that give the set of locally eventually phi-periodic points full measure. We prove the convergence of the mean averages under phi of this measures. We characterize the ergodicity of the limit measures (solving a question posed by Blanchard and Tisseur) and we prove that in the limit phi is a mixture measure theoretical odometers.