Concentration inequalities for the spectral measure of random matrices

Bernard Delyon (Université Rennes 1)

Abstract


We give new exponential inequalities for the spectral measure of random Wishart matrices. These results give in particular useful bounds when these matrices have the form $M=YY^T$, in the case where $Y$ is a $p\times n$ random matrix with independent enties (weaker conditions are also proposed), and $p$ and $n$ are large.

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Pages: 549-562

Publication Date: November 15, 2010

DOI: 10.1214/ECP.v15-1585

References

  1. Bai, Zhidong; Silverstein, Jack W. Spectral analysis of large dimensional random matrices. Second edition. Springer Series in Statistics. Springer, New York, 2010. xvi+551 pp. ISBN: 978-1-4419-0660-1 MR2567175
  2. Boucheron, Stéphane; Lugosi, Gábor; Massart, Pascal. Concentration inequalities using the entropy method. Ann. Probab. 31 (2003), no. 3, 1583--1614. MR1989444 (2004i:60023)
  3. Guionnet, A.; Zeitouni, O. Concentration of the spectral measure for large matrices. Electron. Comm. Probab. 5 (2000), 119--136 (electronic). MR1781846 (2001k:15035)
  4. Guntuboyina, Adityanand; Leeb, Hannes. Concentration of the spectral measure of large Wishart matrices with dependent entries. Electron. Commun. Probab. 14 (2009), 334--342. MR2535081 (Review)
  5. Kriegl, Andreas; Losik, Mark; Michor, Peter W. Choosing roots of polynomials smoothly. II. Israel J. Math. 139 (2004), 183--188. MR2041790 (2005c:58016)
  6. McDiarmid, Colin; On the method of bounded differences, Surveys in combinatorics, 1989 (Norwich, 1989), London Math. Soc. Lecture Note Ser. 141 (1989), 148--188., Cambridge Univ. Press. MR1036755 (91e:05077)
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