Our derivation of (2.4)-(2.8) uses a recent result of Nagao and Slevin [8] to obtain (2.4), and the theory of Tracy and Widom [9] to obtain (2.7). Nagao and Slevin consider the random matrix ensemble with unitary symmetry defined by the eigenvalue p.d.f.

They prove that in the thermodynamic limit, with each scaled so that the bulk density is , the corresponding n-particle distribution is given by

where is given by (2.5) (for , , in the denominator needs to be replaced by , however below we will only consider the case ).
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