Three-dimensional Gaussian fluctuations of spectra of overlapping stochastic Wishart matrices Academic Article uri icon

abstract

  • In [I. Dumitriu and E. Paquette, Spectra of overlapping Wishart matrices and the gaussian free field, Random Matrices: Theory Appl.07(2) (2018) 1850003], 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 [A. Borodin, CLT for spectra of submatrices of Wigner random matrices, Moscow Math. J.14(1) (2014) 2938] for stochastic Wigner matrices.

published proceedings

  • RANDOM MATRICES-THEORY AND APPLICATIONS

author list (cited authors)

  • Kuan, J., & Zhou, Z.

citation count

  • 0

complete list of authors

  • Kuan, Jeffrey||Zhou, Zhengye

publication date

  • January 2022