Covariance formulas for fluctuations of linear spectral statistics for Wigner matrices with few moments
Mathematical Physics Seminar
7th December 2018, 2:00 pm – 3:00 pm
Howard House, 4th Floor Seminar Room
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.