AUEB Stats Seminars 7/4/2023: An information-theoretic Central Limit Theorem for discrete random variables by Lampros Gavalakis (Gustave Eiffel University, France)

AUEB STATS SEMINARS 2023

Lampros Gavalakis,
Gustave Eiffel University, France


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

FRIDAY 7/4/2023
12:00

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.