FLUCTUATIONS OF THE STIELTJES TRANSFORM OF THE EMPIRICAL SPECTRAL DISTRIBUTION OF SELFADJOINT POLYNOMIALS IN WIGNER AND DETERMINISTIC DIAGONAL MATRICES - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2021

FLUCTUATIONS OF THE STIELTJES TRANSFORM OF THE EMPIRICAL SPECTRAL DISTRIBUTION OF SELFADJOINT POLYNOMIALS IN WIGNER AND DETERMINISTIC DIAGONAL MATRICES

Résumé

We investigate the fluctuations around the mean of the Stieltjes transform of the empirical spectral distribution of any selfadjoint noncommutative polynomial in a Wigner matrix and a deterministic diagonal matrix. We obtain the convergence in distribution to a centred complex Gaussian process whose covariance is expressed in terms of operator-valued subordination functions.
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Dates et versions

hal-03357405 , version 1 (20-07-2021)
hal-03357405 , version 2 (28-09-2021)

Identifiants

Citer

Serban Belinschi, Mireille Capitaine, Sandrine Dallaporta, Maxime Fevrier. FLUCTUATIONS OF THE STIELTJES TRANSFORM OF THE EMPIRICAL SPECTRAL DISTRIBUTION OF SELFADJOINT POLYNOMIALS IN WIGNER AND DETERMINISTIC DIAGONAL MATRICES. 2021. ⟨hal-03357405v1⟩
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