BRICS 2021 — Venue LH2 | Invited Talk by Prof. Manjunath Krishnapur
Channel: BRICS Mathematics Conference 2021
Date: 2021-12-07

Title: On the KMT theorem for simple symmetric random walks
Speaker: Manjunath Krishnapur, IISc Bangalore

Abstract: A fundamental result in probability due to Komlos-Major-Tusnady says that a simple symmetric random walk on integers can be coupled with a Brownian motion in such a way that up to time n, they are within log(n) distance of each other. This has been generalized and extended to other settings, but the basic result is still of much interest and new simplified proofs appear periodically. A new kind of proof, using methods akin to Stein’s method was found by Sourav Chatterjee about ten years ago. We present a simplified version of this proof that involves coupling two nearest neighbor Markov chains on integers.