Outlier eigenvalue fluctuations of perturbed iid matrices

2015/07/06 by Anand Bharathwaj Rajagopalan, Rajagopalan, Anand B.
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.1507.01441

openalex publication_date 2015/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is known that in various random matrix models, large perturbations create outlier eigenvalues which lie, asymptotically, in the complement of the support of the limiting spectral density. This paper is concerned with fluctuations of these outlier eigenvalues of iid matrices X_n under bounded rank and bounded operator norm perturbations A_n, namely with λ((X_n)/(√(n))+A_n)-λ(A_n). The perturbations we consider are allowed to be of arbitrary Jordan type and have (left and right) eigenvectors satisfying a mild condition. We obtain the joint convergence of the (normalized) asymptotic fluctuations of the outlier eigenvalues in this setting with a unified approach.

Citations

• THE GENERALISED PRODUCT MOMENT DISTRIBUTION IN SAMPLES FROM A NORMAL MULTIVARIATE POPULATION

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