Interior eigenvalue density of Jordan matrices with random perturbations

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.
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Submitted on : Tuesday, December 12, 2017 - 11:24:22 AM
Last modification on : Wednesday, January 23, 2019 - 2:39:26 PM

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Johannes Sjöstrand, Martin Vogel. Interior eigenvalue density of Jordan matrices with random perturbations. Mats Andersson; Jan Boman; Christer Kiselman; Pavel Kurasov; Ragnar Sigurdsson. Analysis meets geometry. The Mikael Passare Memorial Volume, Birkhäuser; Springer, pp.439-466, 2017, Trends in Mathematics, 978-3-319-52469-6. ⟨10.1007/978-3-319-52471-9_24⟩. ⟨hal-01661782⟩

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