Intrinsic entropies of log-concave distributions

Abstract

<lb>The entropy of a random variable is well-known to equal the exponential growth rate of the<lb>volumes of its typical sets. In this paper, we show that for any log-concave random variable<lb>X , the sequence of the ⌊nθ⌋th intrinsic volumes of the typical sets of X in dimensions n ≥ 1<lb>grows exponentially with a well-defined rate. We denote this rate by hX(θ), and call it the θ th<lb>intrinsic entropy of X . We show that hX(θ) is a continuous function of θ over the range [0, 1],<lb>thereby providing a smooth interpolation between the values 0 and h(X) at the endpoints 0 and<lb>1, respectively.<lb>

Cite this paper

@article{Jog2017IntrinsicEO, title={Intrinsic entropies of log-concave distributions}, author={Varun Jog and Venkat Anantharam}, journal={CoRR}, year={2017}, volume={abs/1702.01203} }