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- W2949252910 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 $lfloor ntheta rfloor^{text{th}}$ intrinsic volumes of the typical sets of $X$ in dimensions $n geq 1$ grows exponentially with a well-defined rate. We denote this rate by $h_X(theta)$, and call it the $theta^{text{th}}$ intrinsic entropy of $X$. We show that $h_X(theta)$ is a continuous function of $theta$ over the range $[0,1]$, thereby providing a smooth interpolation between the values 0 and $h(X)$ at the endpoints 0 and 1, respectively." @default.
- W2949252910 created "2019-06-27" @default.
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- W2949252910 date "2017-02-03" @default.
- W2949252910 modified "2023-09-27" @default.
- W2949252910 title "Intrinsic entropies of log-concave distributions" @default.
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