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SUMMARY:On special function positive solutions of the first discrete Painl
 evé hierarchy  - Ana Loureiro (University of Kent)
DTSTART:20221104T112000Z
DTEND:20221104T121000Z
UID:TALK185246@talks.cam.ac.uk
DESCRIPTION:The recurrence coefficients in the three-term recurrence relat
 ion of a polynomial sequence orthogonal with respect to a quartic or a sex
 tic Freud weights satisfy a forth order discrete equation which is a membe
 r of the first discrete Painlev&eacute\; hierarchy. They also satisfy a co
 upled system of second-order\, nonlinear differential equations. Such orth
 ogonality weights also arise in the context of Hermitian matrix models and
  random symmetric matrix ensembles. In this talk I will report on properti
 es of such recurrence coefficients and explain how the study may inform on
  the study of recurrence coefficients associated with higher order Freud w
 eights. The emphasis will be on their asymptotic properties.&nbsp\;\n&nbsp
 \;\nCollaborators: Peter Clarkson (University of Kent) and Kerstin Jordaan
  (University of South Africa)
LOCATION:Seminar Room 1\, Newton Institute
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