Dimensional behaviour of entropy and information |
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Authors: | Sergey Bobkov Mokshay Madiman |
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Institution: | 1. School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA;2. Department of Statistics, Yale University, New Haven, CT 06511, USA |
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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. |
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