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:20260421T173350Z UID:BPS/7 DESCRIPTION:Title: Two proofs of the KMT theorems\nby Manjunath Krishnapur (Indian Institute of Science\, Bangalore) as part of Bangalore Probability Seminar\n\n\nAbst ract\nThe Komlós-Major-Tusnády theorem for simple symmetric random walk asserts that up to n steps\, its path can be coupled to stay within distan ce log(n) of a Brownian motion run for time n. A second KMT theorem says t hat the empirical distribution function of n i.i.d. uniform random variabl es on [0\,1] can be coupled to stay within log(n)/√n distance of a Brown ian bridge.\n\nAdding the idea of Cauchy criterion to existing proof archi tectures\, we obtain (perhaps) simpler proofs of the above theorems. The f irst proof compares two Binomial distributions by combinatorial methods. T he second proof compares Binomial and hypergeometric distributions among themselves by coupling Markov chains with these as stationary distribution s. This is based on Chatterjee's proof via a form of Stein's method.\n\nTh e first lecture will give an overview and the essence of the first proof. The second lecture will give an account of the second proof. Despite the s tatement of the main results\, much of the lecture should be accessible ( without knowing about Brownian motion) to those who know Markov chains.\n LOCATION:https://researchseminars.org/talk/BPS/7/ END:VEVENT END:VCALENDAR