Spiked random matrix models arise when a matrix of interest (e.g. a sample covariance matrix) is corrupted by noise. In this context, one would like to understand the largest eigenvalues of the matrix (and the corresponding eigenvectors) to perform a principal component analysis. We will discuss the regime in which the random perturbation is of the same size (in the appropriate sense) as the original matrix, on the example of beta Gaussian random matrix ensembles with one spike. In this case, the process of largest eigenvalues can be described by a functional of a reflected Brownian motion. This is joint work with Pierre Yves Gaudreau Lamarre.


Speaker(s): Misha Shkolnikov (Princeton)