### 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.

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