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_(0,s), via Dyson's Coulomb Fluid approach. For the α=0 Unitary-Laguerre Ensemble, we recover the exact spacing distribution found by both Edelman and Forrester, while for α≠ 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 Painlevé transcendent. In the same approximation, the
more » ... next leading term, due to a "finite temperature" perturbation (≠ 2), is found.
doi:10.1088/0305-4470/27/11/011 fatcat:35faggfehjfz7hedgixcdd5y5y