Noncentral Limit Theorem for Large Wishart Matrices with Hermite Entries

. We analyze the limit behavior of the Wishart matrix W n,d = X n,d X Tn,d constructed from an n × d random matrix X n,d whose entries are given by the increments of the Hermite process. These entries are correlated on the same row, independent from one row to another and their probability distribution is di ff erent on di ff erent rows. We prove that the Wishart matrix converges in law, as d → ∞ , to a diagonal random matrix whose diagonal elements are random variables in the second Wiener chaos. We also estimate the Wasserstein distance associated to this convergence.