For Gaussian i.i.d. data, the singular-value spectrum of the empirical cross-covariance is governed by a cubic Stieltjes equation, with simplified edge formulas in several asymptotic regimes.
(A13), reduces to: h3z2pX 2 + h2z (pX (1 − pX ) +pX (1 − pX )) + h (1 − pX )(1 − pX ) − zpX 2 + p2 X = 0, (B1) and the discriminant (Eq
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Distribution of singular values in large sample cross-covariance matrices
For Gaussian i.i.d. data, the singular-value spectrum of the empirical cross-covariance is governed by a cubic Stieltjes equation, with simplified edge formulas in several asymptotic regimes.