Level Crossing in Random Matrices: I. Random perturbation of a fixed matrix

B. Shapiro; K. Zarembo

doi:10.1088/1751-8121/aa5186

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arXiv · 1603.03307

Level Crossing in Random Matrices: I. Random perturbation of a fixed matrix

B. Shapiro·K. Zarembo

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Abstract

We consider level crossing in a matrix family $H=H_0+λV$ where $H_0$ is a fixed $N\times N$ matrix and $V$ belongs to one of the standard Gaussian random matrix ensembles. We study the probability distribution of level crossing points in the complex plane of $λ$, for which we obtain a number of exact, asymptotic and approximate formulas.

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B. Shapiro, K. Zarembo. 2016-12-10. Level Crossing in Random Matrices: I. Random perturbation of a fixed matrix. https://doi.org/10.1088/1751-8121%2Faa5186

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