A1438
Title: On spectrum of sample correlated matrices from large fold tensor vectors
Authors: Wangjun Yuan - Southern University of Science and Technology (China) [presenting]
Abstract: The limiting spectral distribution of the sample correlation matrix is investigated, whose sample vectors are $k$-fold tensor products of $n$-dimensional vectors with i.i.d. entries. The focus is on the limiting regime $n,k \to \infty$ with $k = o(n)$, and it is shown that the limiting spectral distribution is the Marcenko-Pastur law. As a consequence, it is shown that the limiting spectral distribution of the Wishart matrix from the $k$-fold tensor product of independent uniformly distributed unit vectors in $\mathbb C^n$ is the Marcenko-Pastur law.
