Level-spacing distributions of the Gaussian unitary random matrix ensemble

Abstract

Level-spacing distributions of the Gaussian Unitary Ensemble (GUE) of random matrix theory are expressed in terms of solutions of coupled differential equations. Series solutions up to order 50 in the level spacing are obtained, thus providing a very good description of the small-spacing part of the level-spacing distribution, which can be used to make comparisons with experimental or numerical data. The level-spacing distributions can be obtained by solving the system of differential equations numerically.

arXiv commentThe series expansions discussed in this paper are available as Mathematica code at http://mcs.open.ac.uk/ugg2/RMT/LevelSpacingGUE.m (16kB)

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Cited by in corpus (6)

• Non-interacting fermions at finite temperature in a $d$-dimensional trap: universal correlations
• Discrete Painlevé equations and random matrix averages
• Nearest-neigbor spacing distributions of the beta-Hermite ensemble of random matrices
• Statistics of fermions in a $d$-dimensional box near a hard wall
• Hole probability for noninteracting fermions in a $d$-dimensional trap
• Surmise for random matrices' level spacing distributions beyond nearest-neighbors