Electronic Journal of Probability

Asymptotic freeness for rectangular random matrices and large deviations for sample covariance matrices with sub-Gaussian tails

Benjamin Groux

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We establish a large deviation principle for the empirical spectral measure of a sample covariance matrix with sub-Gaussian entries, which extends Bordenave and Caputo’s result for Wigner matrices having the same type of entries [7]. To this aim, we need to establish an asymptotic freeness result for rectangular free convolution, more precisely, we give a bound in the subordination formula for information-plus-noise matrices.

Article information

Electron. J. Probab., Volume 22 (2017), paper no. 53, 40 pp.

Received: 15 May 2015
Accepted: 9 September 2016
First available in Project Euclid: 21 June 2017

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Zentralblatt MATH identifier

Primary: 60B20: Random matrices (probabilistic aspects; for algebraic aspects see 15B52) 46L54: Free probability and free operator algebras 60F10: Large deviations

random matrices large deviations free convolution subordination property spectral measure Stieltjes transform information-plus-noise model

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Groux, Benjamin. Asymptotic freeness for rectangular random matrices and large deviations for sample covariance matrices with sub-Gaussian tails. Electron. J. Probab. 22 (2017), paper no. 53, 40 pp. doi:10.1214/17-EJP4326. https://projecteuclid.org/euclid.ejp/1498010466

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