Beyond universality in random matrix theory

Understand

In order to have a better understanding of finite random matrices with non-Gaussian entries, we study the $1/N$ expansion of local eigenvalue statistics in both the bulk and at the hard edge of the spectrum of random matrices.

• This gives valuable information about the smallest singular value not seen in universality laws.
• In particular, we show the dependence on the fourth moment (or the kurtosis) of the entries.
• This work makes use of the so-called complex Gaussian divisible ensembles for both Wigner and sample covariance matrices.