2000 character limit reached
Entropy and thinning of discrete random variables (1510.05390v3)
Published 19 Oct 2015 in math.PR, cs.IT, and math.IT
Abstract: We describe five types of results concerning information and concentration of discrete random variables, and relationships between them, motivated by their counterparts in the continuous case. The results we consider are information theoretic approaches to Poisson approximation, the maximum entropy property of the Poisson distribution, discrete concentration (Poincar\'{e} and logarithmic Sobolev) inequalities, monotonicity of entropy and concavity of entropy in the Shepp--Olkin regime.