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

100%

Ball K., Nguyen V.

Studia Mathematica

2012

tom 213

nr 1

81-96

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).

Logarithmically concave functions and sections of convex sets in $R^{n}$

60%

Ball K.

Studia Mathematica

1988

tom 88

nr 1

69-84

Ograniczanie wyników

2 Studia Mathematica

2 Ball K.

1 Nguyen V.

1 2012

1 1988

Wyniki wyszukiwania

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

Logarithmically concave functions and sections of convex sets in $R^{n}$