BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Manjunath Krishnapur (Indian Institute of Science\, Bangalore) DTSTART:20211111T060000Z DTEND:20211111T070000Z DTSTAMP:20260423T004636Z UID:ARCSIN/6 DESCRIPTION:Title: F ree probability\, free convolution and associated combinatorics of non-cro ssing partitions\nby Manjunath Krishnapur (Indian Institute of Science \, Bangalore) as part of ARCSIN - Algebra\, Representations\, Combinatoric s and Symmetric functions in INdia\n\n\nAbstract\nThis is an expository ta lk on free probability\, which is a part of operator theory with very stro ng parallels to probability theory. In particular\, we shall focus on free convolution\, which is a binary operation on measures on the real line th at is different from the usual convolution that arises when one adds indep endent random variables. Getting rid of analysis and expressing everything algebraically\, the difference between the two forms of convolution arise s from the difference between the lattice of all set partitions of a finit e set and the lattice of all non-crossing set partitions of the same. We w ould also like to explain how free convolution arises in random matrix the ory (what are the eigenvalues of the sum of two large matrices?) and in as ymptotic representation theory of symmetric groups (what are the Littlewoo d-Richardson coefficients of large partitions?). \n\nNot much knowledge o f probability will be assumed. We shall refer to Bernoulli and Gaussian ra ndom variables\, independence and convolution\, central limit theorem\, ma inly to explain the analogies. The talk should be accessible to advanced u ndergraduates.\n LOCATION:https://researchseminars.org/talk/ARCSIN/6/ END:VEVENT END:VCALENDAR