BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Mary Wootters (Stanford University) DTSTART:20201113T160500Z DTEND:20201113T170500Z DTSTAMP:20260423T005740Z UID:sss/13 DESCRIPTION:Title: Sha rp Thresholds for Random Subspaces\, and Applications\nby Mary Wootter s (Stanford University) as part of Stochastics and Statistics Seminar Seri es\n\n\nAbstract\nAbstract: What combinatorial properties are likely to be satisfied by a random subspace over a finite field? For example\, is it l ikely that not too many points lie in any Hamming ball? What about any cub e? We show that there is a sharp threshold on the dimension of the subspa ce at which the answers to these questions change from “extremely likely ” to “extremely unlikely\,” and moreover we give a simple characteri zation of this threshold for different properties. Our motivation comes fr om error correcting codes\, and we use this characterization to make progr ess on the questions of list-decoding and list-recovery for random linear codes\, and also to establish the list-decodability of random Low Density Parity-Check (LDPC) codes.\n\nThis talk is based on the joint works with V enkatesan Guruswami\, Ray Li\, Jonathan Mosheiff\, Nicolas Resch\, Noga Ro n-Zewi\, and Shashwat Silas.\nEvent Navigation\n LOCATION:https://researchseminars.org/talk/sss/13/ END:VEVENT END:VCALENDAR