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We refine the recent breakthrough technique of Klartag and Lehec to obtain an improved polylogarithmic bound for the KLS constant.
Isoperimetric problems for convex bodies and a localization lemma
R. Kannan, L. Lovász, and M. Simonovits · 1995
Earlier work this paper cites.
The (b) conjecture for the gaussian measure of dilates of symmetric convex sets and related problems
Dario Cordero-Erausquin, Matthieu Fradelizi, and Bernard Maurey · 2004
Earlier work this paper cites.
Large deviations of vector-valued martingales in 2-smooth normed spaces
Anatoli Juditsky and Arkadii S Nemirovski · 2008
Earlier work this paper cites.
Thin shell implies spectral gap up to polylog via a stochastic localization scheme
R. Eldan · 2013
Earlier work this paper cites.
Bounding the norm of a log-concave vector via thin-shell estimates
Ronen Eldan and Joseph Lehec · 2014
Cited alongside, same era.
Eldan’s stochastic localization and the kls conjecture: Isoperimetry, concentration and mixing
Yin Tat Lee and Santosh S Vempala · 2016
Cited alongside, same era.
The kannan-lovasz-simonovits conjecture
Y. T. Lee and S. Vempala · 2019
Cited alongside, same era.
A generalized central limit conjecture for convex bodies
Haotian Jiang, Yin Tat Lee, and Santosh S Vempala · 2020
Cited alongside, same era.
An almost constant lower bound of the isoperimetric coefficient in the kls conjecture
Yuansi Chen · 2021
Later among the works it cites.
Reducing isotropy and volume to kls: an o*(n 3 ψ \psi 2) volume algorithm
He Jia, Aditi Laddha, Yin Tat Lee, and Santosh Vempala · 2021
Later among the works it cites.
Bourgain’s slicing problem and kls isoperimetry up to polylog
Bo’az Klartag and Joseph Lehec · 2022
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