Level crossing in random matrices: I. Random perturbation of a fixed matrix. (23rd December 2016)

• Record Type: Journal Article
• Authors: Shapiro, B; Zarembo, K
• Is Part Of: Journal of physics. Volume 50:Number 4(2017)
• Publication Date: 2016-12-23
• Subjects: random matrices -- level crossing -- Gaussian ensembles of random matrices; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/aa5186
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: We consider level crossing in a matrix family H = H 0 + λ V where H 0 is a fixed N × 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.