An Almost Constant Lower Bound of the Isoperimetric Coefficient in the KLS Conjecture

We prove an almost constant lower bound of the isoperimetric coefficient in the KLS conjecture. The lower bound has the dimension dependency d - o d ( 1 ) . When the dimension is large enough, our lower bound is tighter than the previous best bound which has the dimension dependency d - 1 / 4 . Impr...

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Bibliographic Details
Published inGeometric and functional analysis Vol. 31; no. 1; pp. 34 - 61
Main Author Chen, Yuansi
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.02.2021
Springer Nature B.V
Subjects
Algorithms
Analysis
Coefficients
Dependence
Lower bounds
Mathematics
Mathematics and Statistics
Slicing
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Summary:We prove an almost constant lower bound of the isoperimetric coefficient in the KLS conjecture. The lower bound has the dimension dependency d - o d ( 1 ) . When the dimension is large enough, our lower bound is tighter than the previous best bound which has the dimension dependency d - 1 / 4 . Improving the current best lower bound of the isoperimetric coefficient in the KLS conjecture has many implications, including improvements of the current best bounds in Bourgain’s slicing conjecture and in the thin-shell conjecture, better concentration inequalities for Lipschitz functions of log-concave measures and better mixing time bounds for MCMC sampling algorithms on log-concave measures.
Bibliography:ObjectType-Article-1
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content type line 14
ISSN:1016-443X
1420-8970
DOI:10.1007/s00039-021-00558-4