Abstract
We study the eigenvalue distribution of a large Jordan block subject to a small random Gaussian perturbation. A result by E. B. Davies and M. Hager shows that as the dimension of the matrix gets large, with probability close to 1, most of the eigenvalues are close to a circle.
We study the expected eigenvalue density of the perturbed Jordan block in the interior of that circle and give a precise asymptotic description.
Résumé. Nous étudions la distribution de valeurs propres d’un grand bloc de Jordan soumis à une petite perturbation gaussienne aléatoire. Un résultat de E. B. Davies et M. Hager montre que quand la dimension de la matrice devient grande, alors avec probabilité proche de 1, la plupart des valeurs propres sont proches d’un cercle.
Nous étudions la répartitions moyenne des valeurs propres à l’intérieur de ce cercle et nous en donnons une description asymptotique précise.
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Sjöstrand, J., Vogel, M. (2017). Interior Eigenvalue Density of Jordan Matrices with Random Perturbations. In: Andersson, M., Boman, J., Kiselman, C., Kurasov, P., Sigurdsson, R. (eds) Analysis Meets Geometry. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-52471-9_24
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DOI: https://doi.org/10.1007/978-3-319-52471-9_24
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-52469-6
Online ISBN: 978-3-319-52471-9
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