# Discrete Entropy Power Inequalities and Sperner Theory

Thursday, February 12, 2015 - 2:00pm - 3:00pm

Lind 305

Mokshay Madiman (University of Delaware)

The entropy power inequality provides a sharp lower bound on the entropy

of the sum of two independent real-valued random variables, and is an important and basic inequality in information theory and probability. Despite several efforts,only partial results exists for the analogous problem in discrete groups such as the integers. We will describe several analogues of the entropy power inequality for integer-valued random variables, using various notions of symmetrization as well as ideas from Sperner theory (related to large antichains in posets). If time permits, we will also discuss the case of random variables taking values in cyclic groups of prime order. Joint work with Liyao Wang and Jae Oh Woo.

of the sum of two independent real-valued random variables, and is an important and basic inequality in information theory and probability. Despite several efforts,only partial results exists for the analogous problem in discrete groups such as the integers. We will describe several analogues of the entropy power inequality for integer-valued random variables, using various notions of symmetrization as well as ideas from Sperner theory (related to large antichains in posets). If time permits, we will also discuss the case of random variables taking values in cyclic groups of prime order. Joint work with Liyao Wang and Jae Oh Woo.