On the top eigenvalue of heavy-tailed random matrices
On the top eigenvalue of heavy-tailed random matrices
We study the statistics of the largest eigenvalue lambda_max of N x N random matrices with unit variance, but power-law distributed entries, P(M_{ij})~ |M_{ij}|^{-1-mu}. When mu > 4, lambda_max converges to 2 with Tracy-Widom fluctuations of order N^{-2/3}. When mu < 4, lambda_max is of order N^{2/mu-1/2} and is governed …