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The Entropy Per Coordinate of a Random Vector is Highly Constrained Under Convexity Conditions

2011
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IEEE Transactions on Information Theory
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The entropy per coordinate in a log-concave random vector of any dimension with given density at the mode is shown to have a range of just 1. Uniform distributions on convex bodies are at the lower end of this range, the distribution with i.i.d. exponentially distributed coordinates is at the upper end, and the normal is exactly in the middle. Thus, in terms of the amount of randomness as measured by entropy per coordinate, any log-concave random vector of any dimension contains randomness that

doi:10.1109/tit.2011.2158475
fatcat:7jxfcxxma5dapmxq32nev2k55y