A Proof of the Hyperplane Conjecture for a Large Class of Probability Density Functions

For log-concave probability density functions fulfilling c ertain regularity conditions we present a proof of the famoushyperplane conjecture , also known as licing problem, in convex geometry originally stated by J. Bourgain. The proof is based on an entropic formu lation of the hyperplane conjecture given by Bobkov and Madiman and uses a recent result on bounding the Kullback-Leibler divergence by the Wasserstein distance given by Polyanskiy and Wu. Moreover, as a related result we present a lower bound on the differential entropy rate of a specific class of s tationary processes.