On spectral distribution of sample covariance matrices from large dimensional and large k-fold tensor products

We study the eigenvalue distributions for sums of independent rank-one k-fold tensor products large n-dimensional vectors. Previous results in literature assume that k=o(n) and show converge to celebrated Marčenko-Pastur law under appropriate moment conditions on base In this paper, motivated by quantum information theory, we regime where k grows faster, namely k=O(n). sequences have a limit, which is different from law, limit holds if only model. The approach based method moments.