The Marcenko-Pastur law is about asymptotic distributions of eigenvalues. It starts from a simple null model (iid zero-mean Gaussian entries) and derives a distribution for the spectrum. In PCA, this allows a data analyst to select the number of principal components using a p-value cutoff.
Is there a similar law that governs the distribution of correlations in CCA? I want to select the dimension of the latent space(s) using the same strategy as above.
This question is very similar to mine, but it's not answered and it's a little less general. (Asking for a test about any relationship at all is like asking "Is the latent space is zero dimensional" whereas I want to select the dimension). It's also about kernel CCA, and I am content with just plain CCA.