Analytic description of statistics of spectra of quantum graphs

What is it about?

We obtain exact and approximate distributions for various statistical characteristics of quantum spectra by adapting standard semiclassical techniques to spectral expansions. We indicate the connection between the spectral decompositions and the theory of weakly dependent random variables and the relation between the limit theorems for trigonometric sums and the universal statistical properties of the spectra of quantum chaotic systems.

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