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

Abstract

We consider level crossing in a matrix family $H=H_0+\lambda V$ 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 $\lambda$, for which we obtain a number of exact, asymptotic and approximate formulas.

35 pages, 16 figures; v2: Introduction and sec. 3.3 expanded, refs. added

References in corpus (3)

• The Lax conjecture is true
• Wigner-Poisson statistics of topological transitions in a Josephson junction
• Detecting level crossings without looking at the spectrum

Cited by in corpus (3)

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• Level crossing in random matrices. II Random perturbation of a random matrix
• Spectral properties of the Bloch-Torrey operator in three dimensions