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SUMMARY:Multiple orthogonal polynomials in random matrix theory - Arno Kui
 jlaars (KU Leuven)
DTSTART:20240808T100000Z
DTEND:20240808T110000Z
UID:TALK219367@talks.cam.ac.uk
DESCRIPTION:I will give an overview of some of the uses of multiple orthog
 onal polynomials (MOPs) in the theory of random matrices. Multiple orthogo
 nal polynomials have orthogonality properties with respect to several orth
 ogonality measures. They arise as averages of characteristic polynomials i
 n a number of random matrix ensembles\, including random matrices with ext
 ernal source\, two matrix models\, Muttalib-Borodin ensembles\, and normal
  random matrices.\nIn such models\, the limiting behavior of MOPs as their
  degrees tend to infinity is of interest for the eigenvalue behavior as th
 e size of the random matrix increases. In typical examples\, the limiting 
 behavior of the zeros of the MOPs is given in terms of a vector equilibriu
 m problem from logarithmic potential theory. New types of critical behavio
 r and phase transitions appear beyond those that arise in models that are 
 associated with ordinary orthogonal polynomials.
LOCATION:External
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