Workshop Random Matrix Theory and Its Applications I

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Sep 14, 2010
Tuesday

11:30 AM - 12:10 PM		Extreme gaps in the spectrum of Random Matrices Gerard Ben Arous (New York University, Courant Institute)
Location -- Video Abstract I will present a joint work with Paul Bourgade (Harvard) about the extreme gaps between eigenvalues of random matrices. We give the joint limiting law of the smallest gaps for Haar-distributed unitary matrices (CUE) and matrices from the Gaussian Unitary Ensemble. In particular, we show that the smallest gaps when rescaled by N-4/3, are Poissonian and we give the limiting distribution of the kth smallest gap. We also show that the largest gap, when normalized by √log N/N, converges in L^p to a constant for all p > 0. These results are compared with the extreme gaps between zeros of the Riemann zeta function. Supplements -- Show Detail