Abstract
We study two spiked models of random matrices under general frameworks corresponding, respectively, to additive deformation of random symmetric matrices and multiplicative perturbation of random covariance matrices. In both cases, the limiting spectral measure in the direction of an eigenvector of the perturbation leads to old and new results on the coordinates of eigenvectors.
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Acknowledgements
I am very thankful to Nathanaël Enriquez for many suggestions about this work. Many thanks to Maxime Février for numerous insightful discussions and for his careful reading of an earlier version of this paper. I would also like to thank Laurent Ménard for his advices. Finally, I would like to thank the anonymous referee for his relevant comments, which helped the general understanding of the present article.
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Noiry, N. Spectral Measures of Spiked Random Matrices. J Theor Probab 34, 923–952 (2021). https://doi.org/10.1007/s10959-020-00987-1
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DOI: https://doi.org/10.1007/s10959-020-00987-1