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The Kannan-Lov\'asz-Simonovits Conjecture

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arxiv 1807.03465 v1 pith:QR6HN25J submitted 2018-07-10 math.PR cs.DSmath.FA

Yin Tat Lee , Santosh S. Vempala This is my paper · ORCID
classification math.PRcs.DSmath.FA
keywords conjectureasz-simonovitsconstantkannan-lovachievedalgorithmsbestbounds
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The Kannan-Lov\'asz-Simonovits conjecture says that the Cheeger constant of any logconcave density is achieved to within a universal, dimension-independent constant factor by a hyperplane-induced subset. Here we survey the origin and consequences of the conjecture (in geometry, probability, information theory and algorithms) as well as recent progress resulting in the current best bounds. The conjecture has lead to several techniques of general interest.

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Cited by 6 Pith papers

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