Fluctuations of the Stieltjes transform of the empirical spectral distribution of selfadjoint polynomials in Wigner and deterministic diagonal matrices
[HYBRID WORKSHOP] Connections and Introductory Workshop: Universality and Integrability in Random Matrix Theory and Interacting Particle Systems, Part 1 August 23, 2021 - August 27, 2021
Location: SLMath: Online/Virtual
random matrices
free probability
Empirical spectral distribution
Stieltjes transform
Fluctuations
Linearization
Operator-valued subordination
Fluctuations Of The Stieltjes Transform Of The Empirical Spectral Distribution Of Selfadjoint Polynomials In Wigner And Deterministic Diagonal Matrices
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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Fluctuations Of The Stieltjes Transform Of The Empirical Spectral Distribution Of Selfadjoint Polynomials In Wigner And Deterministic Diagonal Matrices
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