2010

Limits of spiked random matrices I

Bloemendal, Alex, Virág, Bálint

Understand

Given a large, high-dimensional sample from a spiked population, the top sample covariance eigenvalue is known to exhibit a phase transition.

We show that the largest eigenvalues have asymptotic distributions near the phase transition in the rank-one spiked real Wishart setting and its general beta analogue, proving a conjecture of Baik, Ben Arous and P\'ech\'e (2005).
We also treat shifted mean Gaussian orthogonal and beta ensembles.
Such results are entirely new in the real case; in the complex case we strengthen existing results by providing optimal scaling assumptions.

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