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Asymptotic level spacing of the Laguerre ensemble: a Coulomb fluid approach

Y Chen, S M Manning
1994 Journal of Physics A: Mathematical and General  
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
more » ... lev\'e transcendent. In the same approximation, the next leading term, due to a "finite temperature" perturbation $(\bt\neq 2)$, is found.
doi:10.1088/0305-4470/27/11/011 fatcat:35faggfehjfz7hedgixcdd5y5y