Seminar: "An information-theoretic Central Limit Theorem for discrete random variables"

AUEB STATISTICS SEMINAR SERIES APRIL 2023

Lampros Gavalakis, Gustave Eiffel University, France

Title: An information-theoretic Central Limit Theorem for discrete random variables

ROOM Τ203, NEW AUEB BUILDING

ABSTRACT: 

Barron (1986) provided an information-theoretic proof of the central limit theorem (CLT) for continuous random variables by showing that the entropy of the standardised sum converges to its maximum. In this talk, we will discuss a new proof of the CLT for discrete random variables using entropy.

We will also briefly discuss the question of monotonicity in this type of convergence and its connection with a conjecture of Tao (2010). Although this conjecture remains open, we will show that it holds true for the special case of log-concave random variables on the integers and discuss possible future directions.

This is joint work with Ioannis Kontoyiannis.