Spectral statistics of the uni-modular ensemble

Abstract

We investigate the spectral statistics of Hermitian matrices in which the elements are chosen uniformly from U (1), called the uni-modular ensemble (UME), in the limit of large matrix size. Using three complimentary methods; a supersymmetric integration method, a combinatorial graph-theoretical analysis and a Brownian motion approach, we are able to derive expressions for 1/N corrections to the mean spectral moments and also analyse the fluctuations about this mean. By addressing the same ensemble from three different point of view, we can critically compare their relative advantages and derive some new results.

35 pages, 3 figures

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• Large-$N$ expansion for the time-delay matrix of ballistic chaotic cavities
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Cited by in corpus (3)

• Random matrices with prescribed eigenvalues and expectation values for random quantum states
• The Statistics of Spectral Shifts due to Finite Rank Perturbations
• Fluctuations of the spectrum in rotationally invariant random matrix ensembles