A universality result for the smallest eigenvalues of certain sample covariance matrices

Details A universality result for the smallest eigenvalues of certain sample covariance matrices A universality result for the smallest eigenvalues of certain sample covariance matrices

2008-12-10

arxiv.org/abs/0812.1961v4

Geom. Funct. Anal. 20-1 (2010), 88-123

Physics

Mathematical Physics

53 pages, 7 figures. To appear in Geom. Funct. Anal

Scientific paper

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 Peche.

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