Intrinsic entropies of log-concave distributions

IEEE Transactions on Information Theory, pp. 93-108, 2018.

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Abstract:

The entropy of a random variable is well-known to equal the exponential growth rate of the volumes of its typical sets. In this paper, we show that for any log-concave random variable X, the sequence of the [nθ]th intrinsic volumes of the typical sets of X in dimensions n ≥ 1 grows exponentially with a well-defined rate. We denote this ra...More

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