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

Keith Ball, and Van Hoang Nguyen. "Entropy jumps for isotropic log-concave random vectors and spectral gap." Studia Mathematica 213.1 (2012): 81-96. <http://eudml.org/doc/285823>.

@article{KeithBall2012,
abstract = {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).},
author = {Keith Ball, Van Hoang Nguyen},
journal = {Studia Mathematica},
keywords = {entropy gap; Fisher information; isotropic constant; isotropic logconcave random vector; spectral gap; Shannon-Stam difference },
language = {eng},
number = {1},
pages = {81-96},
title = {Entropy jumps for isotropic log-concave random vectors and spectral gap},
url = {http://eudml.org/doc/285823},
volume = {213},
year = {2012},
}

TY - JOUR
AU - Keith Ball
AU - Van Hoang Nguyen
TI - Entropy jumps for isotropic log-concave random vectors and spectral gap
JO - Studia Mathematica
PY - 2012
VL - 213
IS - 1
SP - 81
EP - 96
AB - 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).
LA - eng
KW - entropy gap; Fisher information; isotropic constant; isotropic logconcave random vector; spectral gap; Shannon-Stam difference
UR - http://eudml.org/doc/285823
ER -