ASYMPTOTIC LEVEL SPACING OF THE LAGUERRE ENSEMBLE - A COULOMB FLUID APPROACH

We determine the asymptotic level spacing distribution for the Laguerre ensemble in a single-scaled interval, (0, s), containing no levels, E(beta) (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, white for alpha not-equal 0, the leading terms of E2 (0, S), found by Tracy and Widom, are reproduced without the use of the Bessel kernel and the associated Painleve transcendent. In the same approximation, the next leading term, due to a 'finite-temperature' perturbation (beta not-equal 2), is found.