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We develop an information-theoretic perspective on some questions in convexgeometry, providing for instance a new equipartition property for log-concaveprobability measures, some Gaussian comparison results for log-concavemeasures, an entropic formulation of the hyperplane conjecture, and a newreverse entropy power inequality for log-concave measures analogous to V.Milman's reverse Brunn-Minkowski inequality.

Dimensional behaviour of entropy and information