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- W3100551867 abstract "We prove stability estimates for the Shannon-Stam inequality (also known as the entropy-power inequality) for log-concave random vectors in terms of entropy and transportation distance. In particular, we give the first stability estimate for general log-concave random vectors in the following form: for log-concave random vectors $X,Y in mathbb{R}^d$, the deficit in the Shannon-Stam inequality is bounded from below by the expression $$ C left(mathrm{D}left(X||Gright) + mathrm{D}left(Y||Gright)right), $$ where $mathrm{D}left( cdot ~ ||Gright)$ denotes the relative entropy with respect to the standard Gaussian and the constant $C$ depends only on the covariance structures and the spectral gaps of $X$ and $Y$. In the case of uniformly log-concave vectors our analysis gives dimension-free bounds. Our proofs are based on a new approach which uses an entropy-minimizing process from stochastic control theory." @default.
- W3100551867 created "2020-11-23" @default.
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- W3100551867 date "2020-03-11" @default.
- W3100551867 modified "2023-09-24" @default.
- W3100551867 title "Stability of the Shannon–Stam inequality via the Föllmer process" @default.
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- W3100551867 doi "https://doi.org/10.1007/s00440-020-00967-w" @default.
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