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arXiv · 0706.0359

Boundary Conditions for Scaled Random Matrix Ensembles in the Bulk of the Spectrum

A. V. Kitaev·N. S. Witte
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Abstract

A spectral average which generalises the local spacing distribution of the eigenvalues of random $ N\times N $ hermitian matrices in the bulk of their spectrum as $ N\to\infty $ is known to be a $τ$-function of the fifth Painlevé system. This $τ$-function, $ τ(s) $, has generic parameters and is transcendental but is characterised by particular boundary conditions about the singular point $s=0$, which we determine here. When the average reduces to the local spacing distribution we find that $τ$-function is of the separatrix, or partially truncated type.

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BibTeXRIS

A. V. Kitaev, N. S. Witte. 2007-06-04. Boundary Conditions for Scaled Random Matrix Ensembles in the Bulk of the Spectrum. https://doi.org/10.1088/1751-8113/40/42/s16

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