BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ramon van Handel (Princeton) DTSTART:20210917T163000Z DTEND:20210917T173000Z DTSTAMP:20260423T005717Z UID:PatC/41 DESCRIPTION:Title: Sh arp matrix concentration inequalities\nby Ramon van Handel (Princeton) as part of Probability and the City Seminar\n\n\nAbstract\nWhat does the spectrum of a random matrix look like when we make no\nassumption whatsoev er about the covariance pattern of its entries? It may\nappear hopeless t hat anything useful can be said at this level of\ngenerality. Nonetheless\ , a set of tools known as "matrix concentration\ninequalities" makes it po ssible to estimate at least the spectral norm of\nvery general random matr ices up to logarithmic factors in the dimension.\nOn the other hand\, it i s well known that these inequalities fail to yield\nsharp results for even the simplest random matrix models.\n\nIn this talk I will describe a powe rful new class of matrix concentration\ninequalities that achieve optimal results in many situations that are\noutside the reach of classical method s. Our results are easily applicable\nin concrete examples\, and yield det ailed nonasymptotic information on the\nfull spectrum of essentially arbit rarily structured random matrices. These\nnew inequalities arise from an u nexpected phenomenon: the spectrum of\nrandom matrices is accurately captu red by certain predictions of free\nprobability theory under surprisingly minimal assumptions. Our proofs\nquantify the notion that it costs little to be free.\n\nThe talk is based on joint works with Afonso Bandeira and M arch\nBoedihardjo\, and with Tatiana Brailovskaya. No prior background wil l be\nassumed.\n LOCATION:https://researchseminars.org/talk/PatC/41/ END:VEVENT END:VCALENDAR