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 (Poincaré and logarithmic Sobolev) inequalities, monotonicity of entropy and concavity of entropy in the Shepp-Olkin regime.
|Title of host publication||Convexity and concentration|
|Subtitle of host publication||proceedings of the Spring 2015 Semester of the Theme Year in Discrete Structures, IMA Minneapolis|
|Editors||Eric Carlen, Mokshay Madiman, Elisabeth Werner|
|Publication status||Published - 21 Apr 2017|
|Name||The IMA Volumes in Mathematics and its Applications|