BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Justin Salez (Univ. Paris-Dauphine\, Paris) DTSTART:20210412T090000Z DTEND:20210412T110000Z DTSTAMP:20260421T173547Z UID:BPS/30 DESCRIPTION:Title: An entropic interpretation of the cutoff phenomenon for finite Markov chains< /a>\nby Justin Salez (Univ. Paris-Dauphine\, Paris) as part of Bangalore P robability Seminar\n\n\nAbstract\nThe cutoff phenomenon is a sharp phase t ransition in the convergence to equilibrium of certain Markov chains. Disc overed by Aldous\, Diaconis and Shahshahani in the context of card shuffl ing\, it has since then been established on a variety of examples. However \, proving cutoff remains a delicate affair\, which requires a very detail ed knowledge of the chain. Identifying the general mechanisms underlying t his phase transition\, without having to pinpoint its precise location\, r emains one of the most fundamental open problems in the area of mixing tim es.\n\nIn the first part of the lecture\, I will provide a self-contained introduction to this beautiful question\, and present some classical examp les. In the second part\, I will discuss a recent interpretation of the cu toff phenomenon in terms of concentration of entropy\, and show how this c an be used to deduce cutoff for a broad class of Markov chains with non-ne gative curvature\, including random walks on abelian Cayley expanders.\n LOCATION:https://researchseminars.org/talk/BPS/30/ END:VEVENT END:VCALENDAR