Dimensional behaviour of entropy and information
arXiv:1101.3352 · doi:10.1016/j.crma.2011.01.008
Abstract
We develop an information-theoretic perspective on some questions in convex geometry, providing for instance a new equipartition property for log-concave probability measures, some Gaussian comparison results for log-concave measures, an entropic formulation of the hyperplane conjecture, and a new reverse entropy power inequality for log-concave measures analogous to V. Milman's reverse Brunn-Minkowski inequality.
6 pages