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.