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Matrix models for beta-ensembles

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  • UserIrina Nenciu (University of Illinois, Chicago)
  • ClockThursday 15 October 2009, 15:00-16:00
  • HouseMR14, CMS.

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In this talk, I will give a brief overview of both classical and modern ideas related to random matrix theory, with emphasis on beta-ensembles for general beta positive. These random matrices have eigenvalues following the Gibbs distribution for n particles of the Coulomb gas on the unit circle or the real line, at inverse temperature beta. In particular, I will highlight the change of perspective, from the classical unitary ensembles, which incorporate a lot of symmetry, to these new ensembles, which are very sparse, and some of the methods we use in our construction, inspired by orthogonal polynomial theory. Finally, I will present some of the consequences of these constructions, for example their relation to stochastic PDEs.

This talk is part of the Applied and Computational Analysis series.

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