On collision of multiple eigenvalues for matrix-valued Gaussian processes

Abstract

For  real symmetric and  complex Hermitian Gaussian processes  whose values are  d×d matrices, we characterize the conditions under which the probability that at least k eigenvalues  collide is positive for 2≤ k≤ d, and we obtain the Hausdorff dimension of the set of collision times.  This is a joint work with Yimin Xiao and Wangjun Yuan.