Eldan's Stochastic Localization and the KLS Conjecture: Isoperimetry, Concentration and Mixing

Yin Tat Lee, Santosh S. Vempala

We show that the Cheeger constant for $n$-dimensional isotropic logconcave measures is $O(n^{1/4})$, improving on the previous best bound of $O(n^{1/3}\sqrt{\log n}).$ As corollari…