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A Universality Result for the Smallest Eigenvalues of Certain Sample Covariance Matrices

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Abstract

After proper rescaling and under some technical assumptions, the smallest eigenvalue of a sample covariance matrix with aspect ratio bounded away from 1 converges to the Tracy–Widom distribution. This complements the results on the largest eigenvalue, due to Soshnikov and Péché.

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Authors and Affiliations

  1. School of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv, 69978, Israel

    Ohad N. Feldheim & Sasha Sodin

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  1. Ohad N. Feldheim
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  2. Sasha Sodin
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Correspondence to Sasha Sodin.

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The second author is supported in part by the Adams Fellowship Program of the Israel Academy of Sciences and Humanities and by the ISF.

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Feldheim, O.N., Sodin, S. A Universality Result for the Smallest Eigenvalues of Certain Sample Covariance Matrices. Geom. Funct. Anal. 20, 88–123 (2010). https://doi.org/10.1007/s00039-010-0055-x

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