Optimal Concentration of Information Content for Log-Concave Densities

Matthieu Fradelizi (1) , Mokshay Madiman (2) , Liyao Wang (3)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
2 University of Delaware - Department of Mathematical Sciences
3 J. P. Morgan

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).

Mots clés: concentration; information; log-concave; varentropy

Domaines: Analyse fonctionnelle [math.FA]

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⟩