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) 29–38] for stochastic Wigner matrices.

在[我。Dumitriu 和 E. Paquette，重叠 Wishart 矩阵和高斯自由场的光谱，随机矩阵：理论应用。 07 (2) (2018) 1850003]，作者考虑重叠Wishart矩阵的特征值并证明其涨落渐近收敛于高斯自由场。在这个简短的说明中，他们的结果被扩展为表明当矩阵项经历随机演化时，波动渐近收敛到三维高斯场，该场具有明确的等高线积分公式。这类似于 [A. Borodin，维格纳随机矩阵子矩阵谱的 CLT，Moscow Math。J.  14 (1) (2014) 29–38] 随机维格纳矩阵。