Large deviations for the largest eigenvalue of the sum of two random matrices

Alice Guionnet; Mylène Maïda

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arXiv · 1810.02538

Large deviations for the largest eigenvalue of the sum of two random matrices

Alice Guionnet·Mylène Maïda

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Abstract

In this paper, we consider the addition of two matrices in generic position, namely A + U BU * , 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 all the cases when A and B have no outliers.

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BibTeX RIS

Alice Guionnet, Mylène Maïda. 2018-10-05. Large deviations for the largest eigenvalue of the sum of two random matrices. https://arxiv.org/abs/1810.02538

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