On collision of multiple eigenvalues for matrix-valued Gaussian processes

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:502

Article

Song, Jian^1,2  Xiao, Yimin³  Yuan, Wangjun⁴ 

[1] Shandong Univ, Res Ctr Math & Interdisciplinary Sci, Qingdao 266237, Shandong, Peoples R China

[2] Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China

[3] Michigan State Univ, Dept Stat & Probabil, A-413 Wells Hall, E Lansing, MI 48824 USA

[4] Univ Hong Kong, Dept Math, Hong Kong, Peoples R China

关键词: Random matrices;    Gaussian random field;    Gaussian orthogonal ensemble;    Gaussian unitary ensemble;    Hitting probabilities;    Hausdorff dimension;   

DOI  :  10.1016/j.jmaa.2021.125261

来源: Elsevier

【 摘 要 】

For real symmetric and complex Hermitian Gaussian processes whose values are d x 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. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

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