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

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-01680232
Contributor : Imb - Université de Bourgogne <>
Submitted on : Wednesday, January 10, 2018 - 2:39:17 PM
Last modification on : Wednesday, January 23, 2019 - 2:39:26 PM

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  • HAL Id : hal-01680232, version 1
  • ARXIV : 1604.05558

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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, ⟨http://www.kurims.kyoto-u.ac.jp/~kenkyubu/bessatsu.html⟩. ⟨hal-01680232⟩

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