Tues. Stat.Phys. seminar

[Cond.Matt. & Stat.Mech.Section]

JOINT ICTP/SISSA STATISTICAL PHYSICS SEMINAR

 

Tuesday, 26 June   -   11:30 hrs.

 

Luigi Stasi Seminar Room -  ICTP Leonardo Building - 1st floor

 


Pierpaolo VIVO    ( LPTMS, Univ. Paris-Sud )

 

"Top eigenvalue of Cauchy random matrices"

 

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.