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.
|Translated title of the contribution||Dimensional behaviour of entropy and information|
|Number of pages||4|
|Journal||Comptes Rendus Mathematique|
|State||Published - Feb 2011|