Anna Maltsev

Covariance formulas for fluctuations of linear spectral statistics for Wigner matrices with few moments

We examine covariance of the fluctuations of the linear spectral statistics for Wigner matrices with entries that have a finite variance but no finite 4th moment. We obtain a closed form expression for the covariance (previously expressed as a double contour integral) and we compute the relevant integral kernel. We furthermore place it in context by a comparison with a similar covariance arising in the light tailed case, i.e. when the entries have more than 4 moments. This is joint work with Asad Lodhia.