Abstract
In this paper we study the distribution of level crossings for the spectra of linear families where A and B are square matrices independently chosen from some given Gaussian ensemble and is a complex-valued parameter. We formulate a number of theoretical and numerical results for the classical Gaussian ensembles and some of their generalisations. Besides, we present intriguing numerical information about the monodromy distribution in case of linear families for the classical Gaussian ensembles of -matrices.
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