Entropy jumps for isotropic log-concave random vectors and spectral gap

• Autorzy: Keith Ball , Van Hoang Nguyen
• Języki publikacji: EN

Abstrakty

EN

We prove a quantitative dimension-free bound in the Shannon-Stam entropy inequality for the convolution of two log-concave distributions in dimension d in terms of the spectral gap of the density. The method relies on the analysis of the Fisher information production, which is the second derivative of the entropy along the (normalized) heat semigroup. We also discuss consequences of our result in the study of the isotropic constant of log-concave distributions (slicing problem).

Kategorie tematyczne

• 94A17: Measures of information, entropy

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2012
• Tom: 213
• Numer: 1
• Strony: 81-96

Daty

wydano

2012

Twórcy

autor

Keith Ball

• Institute of Mathematics, University of Warwick, Coventry, CV4 7AL, UK

autor

Van Hoang Nguyen

• Institut de Mathématiques de Jussieu, UPMC, 4 place Jussieu, 75252 Paris, France

Identyfikatory

DOI

10.4064/sm213-1-6