Georgia Institute of Technology College of Sciences

Parry proved in 1964 that a mixing subshift of finite type has a unique measure of maximal entropy. Upper semi-continuity of entropy implies that every invariant measure with nearly maximal entropy must be close to the MME in the Wasserstein metric, which metrizes the weak* topology. In 2015, Kadyrov proved an effective uniqueness result that provides a quantitative version of this statement.

I will present joint work with Teena Kumari, in which we prove that Kadyrov's result remains true when the Wasserstein metric is replaced with Ornstein's d-bar metric. This strengthens the qualitative result from Ornstein theory that the MME is finitely determined since it is isomorphic to a Bernoulli shift. I will also discuss connections to recent work by a number of authors on derivatives of the pressure function and Gaussian concentration bounds.