Joint ICTP/SISSA Statistical Physics seminar: "Top eigenvalue of Cauchy random matrices"
Starts 26 Jun 2012 12:30
Ends 26 Jun 2012 20:00
Central European Time
Leonardo da Vinci Building Luigi Stasi Seminar Room
Strada Costiera, 11
I - 34151 Trieste (Italy)
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.