Some distribution functions of the Laguerre ensemble

Abstract

In this paper we revisit the smallest-eigenvalue distribution of the Laguerre ensembles by presenting in closed form certain integrals obtained previously. With this information we compute, using Dyson's continuum approximation, the two-smallest-eigenvalue distribution of the Laguerre ensemble. High-order contributions to the free energies describing these two probabilities in certain scaling limits or β\neq 2, which can be interpreted in this context as an entropic effect, are found.

28 pages. No figures. Including 1 table. Latex

References in corpus (5)

• Level-Spacing Distributions and the Airy Kernel
• Fredholm Determinants, Differential Equations and Matrix Models
• Level-Spacing Distributions and the Bessel Kernel
• Asymptotic Level Spacing of the Laguerre Ensemble: A Coulomb Fluid Approach
• Gap Formation Probability of the $\alpha -$ Ensemble

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