We have obtained the following results. The p.d.f. for the infinite GUE is given in terms of a Fredholm determinant by

where is the integral operator on with kernel

( denotes the Bessel function) and b=1. Furthermore

(here the mean eigenvalue spacing is ), where satisfies the non-linear equation

with b=1, subject to the boundary condition

with b=1 (the parameter b is included above for later convenience). Note that with b=0 (2.7) reduces to (2.2).
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