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

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/FOCS.2017.96

ABSTRACT

We show that the KLS constant for n-dimensional isotropic logconcave measures is O(n

^{1/4}), improving on the current best bound of O(n^{1/3}√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 ℝ^{n}converges in O*(n^{2.5}) 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

CITATIONS