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 ).