Level crossing in random matrices. II Random perturbation of a random matrix
arXiv:1806.08732 · doi:10.1088/1751-8121/ab1733
Abstract
In this paper we study the distribution of level crossings for the spectra of linear families A+lambda B, where A and B are square matrices independently chosen from some given Gaussian ensemble and lambda is a complex-valued parameter. We formulate a number of theoretical and numerical results for the classical Gaussian ensembles and some generalisations. Besides, we present intriguing numerical information about the distribution of monodromy in case of linear families for the classical Gaussian ensembles of 3 * 3 matrices.
arXiv comment27 pages, many figures
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