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Optimal Concentration of Information Content for Log-Concave Densities

Abstract : An elementary proof is provided of sharp bounds for the varentropy of random vectors with log-concave densities, as well as for deviations of the information content from its mean. These bounds significantly improve on the bounds obtained by Bobkov and Madiman (Ann. Probab., 39(4):1528–1543, 2011).
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Matthieu Fradelizi, Mokshay Madiman, Liyao Wang. Optimal Concentration of Information Content for Log-Concave Densities. High dimensional probability VII, The Cargèse Volume, 2016, 978-3-319-40517-9. ⟨hal-01590210⟩

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