Three-dimensional Gaussian fluctuations of spectra of overlapping stochastic Wishart matrices

Abstract

In [DP18], the authors consider eigenvalues of overlapping Wishart matrices and prove that its fluctuations asymptotically convergence to the Gaussian free field. In this brief note, their result is extended to show that when the matrix entries undergo stochastic evolution, the fluctuations asymptotically converge to a three-dimensional Gaussian field, which has an explicit contour integral formula. This is analogous to the result of [Bor14] for stochastic Wigner matrices.