Year: 2026
Type: preprint
Abstract: We study mesoscopic linear spectral statistics for two ensembles of random quantum graphs. These are defined by a discrete graph $G$ and a unitary-matrix-valued function $U(k)$ indexed by directed edges of $G$. The matrix function $U(k)$ is constructed from unitary matrices $U^{(v)}$ indexed by the neighbours of each vertex $v$. The first ensemble is obtained by sampling the underlying discrete graph uniformly from the set of $d$-regular graphs. The second ensemble is obtained by sampling $U^{(v)}$ uniformly from the Haar measure, independently for each vertex. We prove that the variance of a linear spectral statistic in the large graph limit on polynomial mesoscopic scales coincides with that of the Gaussian Orthogonal/Unitary Ensemble.
Source: arXiv (Cornell University)
Authors: Maltsev, Anna, Osman, Mohammed
Institution: University of London
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7167226465
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