On collision of multiple eigenvalues for matrix-valued Gaussian processes

Jian Song; Yimin Xiao; Wangjun Yuan

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arXiv · 2006.15839

On collision of multiple eigenvalues for matrix-valued Gaussian processes

Jian Song·Yimin Xiao·Wangjun Yuan

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Abstract

For real symmetric and complex Hermitian Gaussian processes whose values are $d\times d$ matrices, we characterize the conditions under which the probability that at least $k$ eigenvalues collide is positive for $2\le k\le d$, and we obtain the Hausdorff dimension of the set of collision times.

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Jian Song, Yimin Xiao, Wangjun Yuan. 2020-06-29. On collision of multiple eigenvalues for matrix-valued Gaussian processes. https://arxiv.org/abs/2006.15839

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