Proves Fredholm determinantal identity for tilted Toeplitz minors generalizing BOGC, with bialternant forms, Cauchy-Binet expansions, and asymptotic links to Airy kernel perturbations.
Phase transition of the largest eigenvalue for non-null complex sample covariance matrices
3 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We compute the limiting distributions of the largest eigenvalue of a complex Gaussian sample covariance matrix when both the number of samples and the number of variables in each sample become large. When all but finitely many, say $r$, eigenvalues of the covariance matrix are the same, the dependence of the limiting distribution of the largest eigenvalue of the sample covariance matrix on those distinguished $r$ eigenvalues of the covariance matrix is completely characterized in terms of an infinite sequence of new distribution functions that generalize the Tracy-Widom distributions of the random matrix theory. Especially a phase transition phenomena is observed. Our results also apply to a last passage percolation model and a queuing model.
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2026 3verdicts
UNVERDICTED 3representative citing papers
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A Borodin-Okounkov-Geronimo-Case identity for tilted Toeplitz minors
Proves Fredholm determinantal identity for tilted Toeplitz minors generalizing BOGC, with bialternant forms, Cauchy-Binet expansions, and asymptotic links to Airy kernel perturbations.