Torben Krüger Stability of the Matrix Dyson Equation and Random

Institute for Applied Mathematics, Bonn University
Oberseminar Stochastik
Thursday, 1 December 2016, 16.30
Lipschitz-Saal (LWK 1.016)
Torben Krüger
IST Austria
Stability of the Matrix Dyson Equation and
Random Matrices with Correlations
The resolvent of a large dimensional self-adjoint random matrix
with correlated entries on short scales converges weakly to a
non-random matrix that satisfies the matrix Dyson equation. We
present a comprehensive stability analysis of this nonlinear matrix equation in asymptotically infinite dimensions down to the
length scale of the eigenvalue spacing. This analysis is then
used to show that the local eigenvalue statistics are universal,
i.e. they do not depend on the distribution of the entries of the
random matrix under consideration (Wigner-Dyson-Mehta spectral universality).

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