The stochastic localization technique was first used by Eldan in 2012 to show that the optimal constants (with respect to the dimension) in the thin shell conjecture, and the conjecture by Kannan, Lovasz, and Simonovits (KLS) are equivalent up to logarithmic factors. Since then, it has also found other applications in convex geometry and probability. In particular, Lee and Vempala used it to improve the best known constant in the KLS conjecture.

In this talk, I will continue with the outline of stochastic calculus, and more specifically talk about Ito's formula (in one and several dimensions). If time permits I will describe the stochastic localization scheme which we will investigate in the next part.
Speaker(s): Alon Nishry (University of Michigan)