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Chapitre D'ouvrage Année : 2017

Interior eigenvalue density of large bi-diagonal matrices subject to random perturbations

Martin Vogel

Résumé

The authors study the spectrum of a random perturbation of a bidiagonal Toeplitz matrix. The perturbation matrix has its entries given via independent and identically distributed complex Gaussian random variables, following the standard complex Gaussian law. The perturbation goes with a nonnegative coupling constant, which assumes very small values. The main result describes the average density of eigenvalues of the random perturbation in the interior of certain confocal ellipses.

Dates et versions

hal-01680232 , version 1 (10-01-2018)

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Johannes Sjöstrand, Martin Vogel. Interior eigenvalue density of large bi-diagonal matrices subject to random perturbations. Yoshitsugu Takei; Takashi Aoki; Naofumi Honda; Kiyoomi Kataoka; Tatsuya Koike. Microlocal analysis and singular perturbation theory, B61, Res. Inst. Math. Sci. (RIMS), pp.201-227, 2017, RIMS Kôkyûroku Bessatsu. ⟨hal-01680232⟩
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