Interior eigenvalue density of large bi-diagonal matrices subject to random perturbations Chapitre d’ouvrage - 2017

Johannes Sjöstrand, Martin Vogel

Johannes Sjöstrand, Martin Vogel, « Interior eigenvalue density of large bi-diagonal matrices subject to random perturbations  », in Yoshitsugu Takei, Takashi Aoki, Naofumi Honda, Kiyoomi Kataoka, Tatsuya Koike (eds.), Microlocal analysis and singular perturbation theory, 2017, pp. 201–227. 〈http://www.kurims.kyoto-u.ac.jp/ kenkyubu/bessatsu.html〉

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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