Abstract
In this paper, we consider the addition of two matrices in generic position, namely $A+UBU^{*}$, where $U$ is drawn under the Haar measure on the unitary or the orthogonal group. We show that, under mild conditions on the empirical spectral measures of the deterministic matrices $A$ and $B$, the law of the largest eigenvalue satisfies a large deviation principle, in the scale $N$, with an explicit rate function involving the limit of spherical integrals. We cover in particular the case when $A$ and $B$ have no outliers.
Citation
Alice Guionnet. Mylène Maïda. "Large deviations for the largest eigenvalue of the sum of two random matrices." Electron. J. Probab. 25 1 - 24, 2020. https://doi.org/10.1214/19-EJP405
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