Some distribution functions of the Laguerre ensemble

Physics – Condensed Matter

Scientific paper

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28 pages. No figures. Including 1 table. Latex

Scientific paper

10.1088/0305-4470/29/23/019

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 \beta\neq 2, which can be interpreted in this context as an entropic effect, are found.

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