The so called GUE hypothesis (see e.g. [1]) states that, in a certain limit, the
zeros of the Riemann zeta function on the critical line Re have the
same joint distribution as that of the eigenvalues of a random matrix from
the Gaussian Unitary Ensemble (GUE) of large (formally infinite) dimensional
random Hermitian matrices. Denoting the zeros by , where n
labels the zeros sequentially along the critical line, the GUE hypothesis
applies in the limit , with each scaled by the
mean density of zeros at , so that the mean spacing between zeros is unity (any finite value will
do).