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SUMMARY:Sung-Soo Byun (Seoul National University)
DTSTART:20200910T140000Z
DTEND:20200910T150000Z
DTSTAMP:20260423T021221Z
UID:JIPS/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/JIPS/6/">A n
 on-Hermitian generalisation of the Marchenko-Pastur distribution: from the
  circular law to multi-criticality</a>\nby Sung-Soo Byun (Seoul National U
 niversity) as part of Junior Integrable Probability Seminar\n\n\nAbstract\
 nIn this talk\, I will discuss complex eigenvalues of the product of two r
 ectangular complex Ginibre matrices that are correlated through a non-Herm
 iticity parameter.\n\nIn the first half\, I will present the limiting spec
 tral distribution of the model\, which interpolates between classical resu
 lts for random matrices on the global scale\, the circular law and the Mar
 chenko-Pastur distribution. In the second half\, I will explain the micros
 copic behaviours of the model\, which includes the limiting local correlat
 ion kernel at multi-criticality\, where the interior of the spectrum split
 s into two connected components.\n\nThe global statistics follows from the
  solution of certain equilibrium measure problem and concentration for the
  2D Coulomb gases on Frostman’s equilibrium measure\, whereas the local 
 statistics follows from a saddle point analysis of the kernel of orthogona
 l Laguerre polynomials in the complex plane.\n\nThis is based on joint wor
 k with Gernot Akemann and Nam-Gyu Kang.\n
LOCATION:https://researchseminars.org/talk/JIPS/6/
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