Stable distributions and stable laws for random matrices

报告题目:Stable distributions and stable laws for random matrices

报告专家:张纪元 博士(比利时鲁汶大学)





We consider random matrix ensembles on the set of Hermitian matrices that are heavy tailed, in particular not all moments exist, and that are invariant under the conjugate action of the unitary group. The latter property entails that the eigenvectors are Haar distributed and, therefore, factorise from the eigenvalue statistics. We prove a classification for stable matrix ensembles of this kind of matrices represented in terms of matrices, their eigenvalues and their diagonal entries with the help of the classification of the multivariate stable distributions and the harmonic analysis on symmetric matrix spaces. Moreover, we identify sufficient and necessary conditions for their domains of attraction.


张纪元博士于2021年在澳大利亚墨尔本大学数学与统计学院获得博士学位,同年留校任研究助理。2022年就职于比利时鲁汶大学任博士后至今。研究方向是随机矩阵理论及相关应用,论文发表在Adv. Math. Constr. Approximation, Lett. Math. Phys.等高质量数学物理期刊上。


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