A recent paper by Baik, Ben Arous, and Péché [16] gives theorems for the asymptotics of the distribution of the largest eigenvalue of a sample covariance matrix when the true covariance matrix has a few eigenvalues greater than 1 and the rest equal to 1. This is the situation in genetic data for which there are just a few meaningful axes of variation. Unfortunately the theorems proved are only for the case of data matrices whose entries are complex numbers, but Baik, Ben Arous, and Péché conjecture that the results hold for real data, too. We state a form of the conjecture, which we call the BBP conjecture, and then provide evidence for its applicability to genetics.
