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SUMMARY:Thomas Bothner (University of Bristol)
DTSTART:20201103T153000Z
DTEND:20201103T163000Z
DTSTAMP:20260513T195540Z
UID:OxfordRMT/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OxfordRMT/5/
 ">A threefold way to integrable probabilistic models</a>\nby Thomas Bothne
 r (University of Bristol) as part of Oxford Random Matrix Theory Seminars\
 n\n\nAbstract\nThis talk is intended for a broad math and physics audience
  in particular including students. It will focus on the speaker's recent c
 ontributions to the analysis of the real Ginibre ensemble consisting of sq
 uare real matrices whose entries are i.i.d. standard normal random variabl
 es. In sharp contrast to the complex and quaternion Ginibre ensemble\, rea
 l eigenvalues in the real Ginibre ensemble attain positive likelihood. In 
 turn\, the spectral radius of a real Ginibre matrix follows a different li
 miting law for purely real eigenvalues than for non-real ones. We will sho
 w that the limiting distribution of the largest real eigenvalue admits a c
 losed form expression in terms of a distinguished solution to an inverse s
 cattering problem for the Zakharov-Shabat system. This system is directly 
 related to several of the most interesting nonlinear evolution equations i
 n $1+1$ dimensions which are solvable by the inverse scattering method. Th
 e results of this talk are based on our joint work with Jinho Baik (arXiv:
 1808.02419 and arXiv:2008.01694).\n\nThis seminar will be held via zoom. M
 eeting link will be sent to members of our mailing list (https://lists.mat
 hs.ox.ac.uk/mailman/listinfo/random-matrix-theory-announce) in our weekly 
 announcement on Monday.\n
LOCATION:https://researchseminars.org/talk/OxfordRMT/5/
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