The Kannan-Lov\'asz-Simonovits Conjecture
Probability
2018-07-11 v1 Data Structures and Algorithms
Functional Analysis
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.
Keywords
Cite
@article{arxiv.1807.03465,
title = {The Kannan-Lov\'asz-Simonovits Conjecture},
author = {Yin Tat Lee and Santosh S. Vempala},
journal= {arXiv preprint arXiv:1807.03465},
year = {2018}
}