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UID:35071
DTSTAMP:20190617T085637Z
SUMMARY:Mathematical Physics & Integrable Systems seminar: Thomas Bothner (King's College London)
LOCATION:SR2, Sibson Building (SibSR2)
DESCRIPTION:The real Ginibre ensemble consists of square real matrices whose entries are i.i.d. standardnormal random variables. In sharp contrast to the complex and quaternion Ginibre ensemble,real eigenvalues in the real Ginibre ensemble attain positive likelihood. In turn, the spectralradius of a real Ginibe matrix follows a different limiting law for purely real eigenvaluesthan for non-real ones. Building on previous work by Rider, Sinclair and Poplavskyi, Tribe,Zaboronski, we will show that the limiting distribution of the largest real eigenvalue admits aclosed form expression in terms of a distinguished solution to an inverse scattering problemfor the Zakharov-Shabat system. This system is directly related to several of the mostinteresting nonlinear evolution equations in 1+1 dimensions which are solvable by the inversescattering method, for instance the nonlinear Schroedinger equation. The results of this talkare based on the recent preprint arXiv:1808.02419, joint with Jinho Baik.\n\n
DTSTART:20181127T140000Z
DTEND:20181127T150000Z
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