BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Manjunath Krishnapur (Indian Institute of Science\, Bangalore) DTSTART:20201021T090000Z DTEND:20201021T110000Z DTSTAMP:20260404T150746Z UID:BPS/7 DESCRIPTION:Title: Two proofs of the KMT theorems\nby Manjunath Krishnapur (Indian Ins titute of Science\, Bangalore) as part of Bangalore Probability Seminar\n\ n\nAbstract\nThe Komlós-Major-Tusnády theorem for simple symmetric rando m walk asserts that up to n steps\, its path can be coupled to stay within distance log(n) of a Brownian motion run for time n. A second KMT theorem says that the empirical distribution function of n i.i.d. uniform random variables on [0\,1] can be coupled to stay within log(n)/√n distance of a Brownian bridge.\n\nAdding the idea of Cauchy criterion to existing proo f architectures\, we obtain (perhaps) simpler proofs of the above theorems . The first proof compares two Binomial distributions by combinatorial met hods. The second proof compares Binomial and hypergeometric distributions among themselves by coupling Markov chains with these as stationary distr ibutions. This is based on Chatterjee's proof via a form of Stein's method .\n\nThe first lecture will give an overview and the essence of the first proof. The second lecture will give an account of the second proof. Despit e the statement of the main results\, much of the lecture should be acces sible (without knowing about Brownian motion) to those who know Markov cha ins.\n LOCATION:https://stable.researchseminars.org/talk/BPS/7/ END:VEVENT END:VCALENDAR