The least singular value of R*XT + U*YV, after scaling by N, converges in distribution to 1 - e^{-r^2}, the same limit as for a complex Gaussian matrix.
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Universality of the least singular value for the sum of random matrices
The least singular value of R*XT + U*YV, after scaling by N, converges in distribution to 1 - e^{-r^2}, the same limit as for a complex Gaussian matrix.