Large deviations of the top eigenvalue of large Cauchy random matrices
Large deviations of the top eigenvalue of large Cauchy random matrices
We compute analytically the large deviation tails of the probability density function (pdf) of the top eigenvalue λmax in rotationally invariant and heavy-tailed Cauchy ensembles of N × N matrices for any Dyson index β > 0, where β = 1, 2, 4 correspond, respectively, to orthogonal, unitary and symplectic …