Extreme gaps between eigenvalues of random matrices

• Autores: Gerard Ben Arous, Paul Bourgade
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 41, Nº. 4, 2013, págs. 2648-2681
• Idioma: inglés
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• Resumen

  • This paper studies the extreme gaps between eigenvalues of random matrices. We give the joint limiting law of the smallest gaps for Haar-distributed unitary matrices and matrices from the Gaussian unitary ensemble. In particular, the kth smallest gap, normalized by a factor n−4/3, has a limiting density proportional to x3k−1e−x3. Concerning the largest gaps, normalized by n/logn−−−−√, they converge in Lp to a constant for all p>0. These results are compared with the extreme gaps between zeros of the Riemann zeta function.