A Wegner estimate for Wigner matrices
Anna Maltsev, Benjamin Schlein
TL;DR
This paper reviews recent spectral results for Wigner matrices and introduces a new proof of a Wegner estimate, providing bounds on the probability of eigenvalues appearing in small intervals.
Contribution
It offers a novel proof of the Wegner estimate for Wigner matrices, enhancing understanding of eigenvalue distributions.
Findings
Wegner estimate bounds eigenvalue probabilities
New proof simplifies existing methods
Results applicable to large classes of Wigner matrices
Abstract
In the first part of these notes, we review some of the recent developments in the study of the spectral properties of Wigner matrices. In the second part, we present a new proof of a Wegner estimate for the eigenvalues of a large class of Wigner matrices. The Wegner estimate gives an upper bound for the probability to find an eigenvalue in an interval , proportional to the size of the interval.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Random Matrices and Applications · Mathematical Analysis and Transform Methods