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2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS) (2017)
Berkeley, California, USA
Oct. 15, 2017 to Oct. 17, 2017
ISSN: 0272-5428
ISBN: 978-1-5386-3464-6
pp: 998-1007
ABSTRACT
We show that the KLS constant for n-dimensional isotropic logconcave measures is O(n1/4), improving on the current best bound of O(n1/3√log n). As corollaries we obtain the same improved bound on the thin-shell estimate, Poincaréconstant and Lipschitz concentration constant and an alternative proof of this bound for the isotropic constant; it also follows that the ball walk for sampling from an isotropic logconcave density in ℝn converges in O*(n2.5) steps from a warm start.
INDEX TERMS
computational complexity, random processes, statistical distributions, stochastic processes
CITATION

Y. T. Lee and S. S. Vempala, "Eldan's Stochastic Localization and the KLS Hyperplane Conjecture: An Improved Lower Bound for Expansion," 2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS), Berkeley, California, USA, 2017, pp. 998-1007.
doi:10.1109/FOCS.2017.96
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