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
Abstract: 
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.