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Seminar:
Joint ICTP/SISSA Statistical Physics seminar: "Top eigenvalue of Cauchy random matrices"
26 June 2012 |
Speaker: Pierpaolo VIVO
(LPTMS, Univ. Paris-Sud ) |
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at 11:30
in Leonardo da Vinci Building Luigi Stasi Seminar Room |
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Abstract: I present analytical results on the distribution of the largest eigenvalue for random matrices of the Cauchy type.
Matrices belonging to this ensemble i) have a rotationally invariant weight, and ii) display a spectral density having support on the full real axis, which decays as a power law for x\to\pm\infty.
The distribution exhibits a central regime that is governed by a scaling function (analogous to the Tracy-Widom distribution), flanked on both sides by large deviation tails. The corresponding rate functions are computed analytically using a mapping to a Coulomb gas system with constraints. The analytical results are corroborated by numerical simulations with excellent agreement.
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