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Title:
Fluctuations of the Stieltjes transform of the empirical spectral distribution of selfadjoint polynomials in Wigner and deterministic diagonal matrices
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Abstract:
We will present the following result. When the dimension goes to infinity, the recentered analytic process on nonreal complex numbers of nonnormalized traces of resolvents of any selfadjoint noncommutative polynomial in a Wigner matrix and a deterministic diagonal matrix converges to a centred complex Gaussian process whose covariance is expressed in terms of operator-valued subordination functions in free probability theory. This is a joint work with Serban Belinschi, Sandrine Dallaporta and Maxime Février.
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