Kieffer-Pinsker type formulas for Gibbs measures.

ABSTRACT:  In this talk I will present ongoing work regarding new expressions for entropy and pressure in the context of Gibbs measures defined over countable groups. Our starting point will be the Pinsker formula for the Kolmogorov-Sinai entropy of measure preserving actions of orderable amenable groups. Then, we will consider a formula for pressure that was developed by Marcus-Pavlov (2015) and B. (2018). Next, we will review some techniques based on random orderings, mixing properties of Markov random fields, and percolation theory in order to generalize previous work by introducing what we call a “Kieffer-Pinsker type formula”. Time permitting, we will discuss some applications and establish connections between these results and part of the role that phase transitions play in our understanding of entropy.

Posted on Jul 9, 2020 in Dynamical Systems, Seminars