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math-ph2000★ 3 cited
Exact Wigner surmise type evaluation of the spacing distribution in the bulk of the scaled random matrix ensembles
P. J. Forrester, N. S. Witte
Random matrix ensembles with orthogonal and unitary symmetry correspond to the cases of real symmetric and Hermitian random matrices respectively. We show that the probability dens…
nlin.SI2000★ 27 cited
Painlevé transcendent evaluation of the scaled distribution of the smallest eigenvalue in the Laguerre orthogonal and symplectic ensembles
P. J. Forrester
The scaled distribution of the smallest eigenvalue in the Laguerre orthogonal and symplectic ensembles is evaluated in terms of a Painlevé V transcendent. This same Painlevé V tran…
cond-mat2000★ 13 cited
Analytic properties of the structure function for the one-dimensional one-component log-gas
P. J. Forrester, B. Jancovici, D. S. McAnally
The structure function for the one-dimensional one-component log-gas is the Fourier transform of the charge-charge, or equivalently the density-density, correlation functi…