Dimensional behaviour of entropy and information
  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. 
Sergey Bobkov and Mokshay Madiman
math.FA cs.IT math.IT math.PR