BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Simona Diaconu (Stanford University) DTSTART:20221102T140000Z DTEND:20221102T150000Z DTSTAMP:20260423T021043Z UID:ADPS/4 DESCRIPTION:Title: Met hod of Moments and Edge Eigenvalues\nby Simona Diaconu (Stanford Unive rsity) as part of Abu Dhabi Stochastics Seminar\n\n\nAbstract\nThe method of moments is a classical technique for showing weak convergence and follo ws a simple recipe: for any natural number m\; compute the mth moments of the random variables of interest\, and prove they tend to the mth moment o f the claimed limit (this works for some limiting laws\, including Gaussia n). This approach has been prolific for universality results: for the larg est eigenvalues of random matrices\, justify their asymptotic behavior dep ends solely on a random variable\, show the moments of the latter depend ( asymptotically) on few moments of the former\, and use the Gaussian case t o deduce the limiting behavior. Although Gaussianity can be relaxed consid erably\, some constraints are indispensable: consider a real-valued Wigner matrix with i.i.d. entries. When the fourth moment of the entry distribut ions is infinite (heavy-tailed)\, the largest eigenvalues are known to con verge to Poisson point processes\, whereas when it is finite (light-tailed )\, the limits are the same as for Gaussian orthogonal ensembles. This tal k focuses on a subfamily of edge cases\, distributions at the boundary bet ween heavy- and lighttailed regimes\, and presents a new application of th e method of moments\, one that allows to obtain the asymptotics of the lar gest eigenvalues directly\, without any comparison to the Gaussian case. A byproduct of this result is a connection between the aforementioned subfa mily and two other families\, finite-rank perturbations of Wigner matrices and sparse random matrices.\nThis presentation is based on https://arxiv. org/pdf/2203.08712.pdf.\n LOCATION:https://researchseminars.org/talk/ADPS/4/ END:VEVENT END:VCALENDAR