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2020 Large deviations for the largest eigenvalue of the sum of two random matrices
Alice Guionnet, Mylène Maïda
Electron. J. Probab. 25: 1-24 (2020). DOI: 10.1214/19-EJP405


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.


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Alice Guionnet. Mylène Maïda. "Large deviations for the largest eigenvalue of the sum of two random matrices." Electron. J. Probab. 25 1 - 24, 2020.


Received: 23 November 2018; Accepted: 22 December 2019; Published: 2020
First available in Project Euclid: 5 February 2020

zbMATH: 1440.15035
MathSciNet: MR4073675
Digital Object Identifier: 10.1214/19-EJP405

Primary: 15A52 , 46L54 , 60F10

Keywords: Extreme eigenvalues , Free convolution , large deviations , Random matrix


Vol.25 • 2020
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