Eigenvalue variance bounds for Wigner random matrices
Résumé
This work is concerned with fi nite range bounds on the variance of individual eigenvalues of random Wigner matrices, both in the bulk and at the edge. Relying on the GUE example, which needs to be investigated fi rst, the main bounds are extended to Wigner Hermitian matrices by means of the Tao and Vu Four Moment Theorem and recent localization results by Erdös, Yau and Yin. The case of real Wigner matrices is obtained from interlacing formulas.
Domaines
Probabilités [math.PR]
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