The performance studies of the celebrated Lempel–Ziv coding algorithm have led to some deep insights into the specific entropy and relative entropy of stationary measures on shift spaces. Notable among those is the characterization of the specific entropy of a stochastic source in terms of the exponential asymptotics of recurrence times of a typical signal, and the related characterization of the specific cross entropy in terms of waiting times. These and other related entropic estimators
have found diverse practical applications beyond information theory.
In this talk I will describe a research program dealing with refinements of the mathematical theory of entropic estimators that originated in information theory, and to their theoretical and practical applications.
Based on the joint works with G. Cristadoro, M. Degli Esposti, and R. Raquepas.