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Dimensional behaviour of entropy and information (1101.3352v1)
Published 17 Jan 2011 in math.FA, cs.IT, math.IT, and math.PR
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.