Asymptotic Level Spacing of the Laguerre Ensemble: A Coulomb Fluid Approach

Details Asymptotic Level Spacing of the Laguerre Ensemble: A Coulomb Fluid Approach Asymptotic Level Spacing of the Laguerre Ensemble: A Coulomb Fluid Approach

1993-09-10

arxiv.org/abs/cond-mat/9309010v2

Physics

Condensed Matter

10pp, LaTeX

Scientific paper

10.1088/0305-4470/27/11/011

We determine the asymptotic level spacing distribution for the Laguerre Ensemble in a single scaled interval, $(0,s)$, containing no levels, $E_{\bt}(0,s)$, via Dyson's Coulomb Fluid approach. For the $\alpha=0$ Unitary-Laguerre Ensemble, we recover the exact spacing distribution found by both Edelman and Forrester, while for $\alpha\neq 0$, the leading terms of $E_{2}(0,s)$, found by Tracy and Widom, are reproduced without the use of the Bessel kernel and the associated Painlev\'e transcendent. In the same approximation, the next leading term, due to a ``finite temperature'' perturbation $(\bt\neq 2)$, is found.

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