Entropy jumps for isotropic log-concave random vectors and spectral gap
By Keith Ball, Van Hoang Nguyen. 2012
55 citations recorded by the source corpus.
We prove a quantitative dimension-free bound in the Shannon{Stam en- tropy 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).
Subfields: Electrical and Electronic Engineering
View Paper: https://www.semanticscholar.org/paper/2ef0ca8e63356dac497d98b129f41230b32c7f87
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In Electrical and Electronic Engineering
Citations in the corpus
- Logarithmic bounds for isoperimetry and slices of convex sets (2023, methodology): “The fact that the KLS conjecture implies Bourgain’s slicing conjecture was announced by Ball in 2003; the proof, using the heat equation and yielding the estimate Ln ≤ exp(Cψ(2) n), was published in the work of Ball and Nguyen [3].”