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DTSTART:19700329T010000
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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Multiple orthogonal polynomials in random matrix t
heory - Arno Kuijlaars (KU Leuven)
DTSTART;TZID=Europe/London:20240808T110000
DTEND;TZID=Europe/London:20240808T120000
UID:TALK219367AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/219367
DESCRIPTION:I will give an overview of some of the uses of mul
tiple orthogonal polynomials (MOPs) in the theory
of random matrices. Multiple orthogonal polynomial
s have orthogonality properties with respect to se
veral orthogonality measures. They arise as averag
es of characteristic polynomials in a number of ra
ndom matrix ensembles\, including random matrices
with external source\, two matrix models\, Muttali
b-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 the size of the random
matrix increases. In typical examples\, the limit
ing behavior of the zeros of the MOPs is given in
terms of a vector equilibrium problem from logarit
hmic potential theory. New types of critical behav
ior and phase transitions appear beyond those that
arise in models that are associated with ordinary
orthogonal polynomials.
LOCATION:External
CONTACT:
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