Multiple collisions of eigenvalues and singular values of matrix Gaussian field

2024/07/12 by Yuan, Wangjun · 1 citation
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2407.09070

Abstract

Let X^β be a real symmetric or complex Hermitian matrix whose entries are independent Gaussian random fields. We provide the sufficient and necessary conditions such that multiple collisions of eigenvalue processes of A^β+ T_βX^βT_β^* occur with positive probability. In addition, for a real or complex rectangular matrix W^β with independent Gaussian random field entries, we obtain the sufficient and necessary conditions under which the probability of multiple collisions of non-trivial singular value processes of B^β+ T_βW^β T_β is positive. In both cases, the size of the set of collision times is characterized via Hausdorff dimension.

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