Statistical Properties of Quantum Graph Spectra

A general analytical approach to the statistical description of quantum graph spectra based on the exact periodic orbit expansions of quantum levels is discussed. The exact and approximate expressions obtained in \cite{Anima} for the probability distribution functions using the spectral hierarchy method are analyzed. In addition, the mechanism of appearance of the universal statistical properties of spectral fluctuations of quantum-chaotic systems is considered in terms of the semiclassical theory of periodic orbits.Comment: 14 pages, 3 fi