BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Roger Van Peski (MIT) DTSTART:20220401T163000Z DTEND:20220401T173000Z DTSTAMP:20260423T005833Z UID:PatC/60 DESCRIPTION:Title: p- adic random matrices and particle systems\nby Roger Van Peski (MIT) as part of Probability and the City Seminar\n\n\nAbstract\nRandom p-adic mat rices have been studied since the late 1980s as natural models for random groups appearing in number theory and combinatorics. Recently it has also become clear that the theory has close structural parallels with singular values of complex random matrices\, bringing new techniques from integrabl e probability and motivating new questions. After outlining this area (no background in p-adic matrices will be assumed)\, I will discuss results on the distribution of analogues of singular values for products of many ran dom p-adic matrices. Both prelimit and limit objects exhibit much more spa tial independence than their analogues for complex matrices\, often with s urprising results. In different regimes we can prove Gaussian limits\, an intriguing new discrete Poisson-type local limit (yielding a local interac ting particle system on $\\mathbb{Z}$ similar to $q$-TASEP)\, and converge nce of global bulk fluctuations to a certain explicit Gaussian process.\n LOCATION:https://researchseminars.org/talk/PatC/60/ END:VEVENT END:VCALENDAR