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SUMMARY:Matrix models for beta-ensembles - Irina Nenciu (University of Ill
 inois\, Chicago)
DTSTART:20091015T140000Z
DTEND:20091015T150000Z
UID:TALK20775@talks.cam.ac.uk
CONTACT:6743
DESCRIPTION:In this talk\, I will give a brief overview of both classical 
 and modern ideas related to random matrix theory\, with emphasis on beta-e
 nsembles for general beta positive. These random matrices have eigenvalues
  following the Gibbs distribution for n particles of the Coulomb gas on th
 e unit circle or the real line\, at inverse temperature beta. In particula
 r\, I will highlight the change of perspective\, from the classical unitar
 y ensembles\, which incorporate a lot of symmetry\, to these new ensembles
 \, which are very sparse\, and some of the methods we use in our construct
 ion\, inspired by orthogonal polynomial theory. Finally\, I will present s
 ome of the consequences of these constructions\, for example their relatio
 n to stochastic PDEs.
LOCATION:MR14\, CMS
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