The Kannan-Lov\'asz-Simonovits Conjecture

Yin Tat Lee; Santosh S. Vempala

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arXiv · 1807.03465

The Kannan-Lov\'asz-Simonovits Conjecture

Yin Tat Lee·Santosh S. Vempala

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Abstract

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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Yin Tat Lee, Santosh S. Vempala. 2018-07-10. The Kannan-Lov\'asz-Simonovits Conjecture. https://arxiv.org/abs/1807.03465

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