The Gaussian law reigns supreme in the information theory of analog random variables leading to closed-form expressions for information measures and extremality properties possessing great pedagogical value. In this talk, we will see that a number of those information theoretic results find elegant counterparts for Cauchy distributions. The talk introduces some new concepts such as that of equivalent pairs of probability measures and the strength of real-valued random variables, which find interesting applications in the context of Cauchy random variables.

Sergio Verdu received the Telecommunications Engineering degree from the Universitat Politecnica de Barcelona in 1980, and the Ph.D. degree in Electrical Engineering from the University of Illinois at Urbana-Champaign in 1984. He was on the faculty of Princeton University from 1984 to 2018. He is the recipient of the 2007 Claude E. Shannon Award, and the 2008 IEEE Richard W. Hamming Medal. He is an elected member of both the National Academy of Engineering and the National Academy of Sciences of the United States, and a corresponding member of the Real Academia de Ingenieria of Spain. He was awarded a Doctorate Honoris Causa from the Universitat Politecnica de Catalunya in 2005.