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Beta ensembles and diffusion

Mathematical Physics & Probability

Speaker: Brian Rider, University of Colorado at Boulder
Location: 1147 MSB
Start time: Tue, Nov 14 2006, 2:10PM

We prove that the largest eigenvalues of the general beta-ensemble of Random Matrix Theory, properly centered and scaled, converge in distribution to the law of the low lying eigenvalues of a random Schroedinger opertor with White Noise potential. Based on this convergence, we provide a new characterization of the Tracy-Widom type laws (for all beta) in terms of the explosion probability of a one-dimensional diffusion.