Plotting the pair correlation function for the zeta zeros /GUE

Question

I am making a shameless request for instructions on how to plot this:

from this page. I can see from here that normalizing the zeros is given by $\delta(n)=(\gamma_{n+1}-\gamma_{n})\dfrac{\log(\gamma_{n}/2\pi)}{2\pi},$ where $\gamma_{n}=\Im\ n$th zeta zero. I cannot, for the life of me however, seem to fathom how to plot its corresponding pair correlation.

To plot this

would be an added bonus, but I can't find the reference to 4.19 anywhere.

Any information on how to plot the pair correlation for random Hermitian matrices, given by something like

n = 100; m = # + ConjugateTranspose[#] &@RandomComplex[{0, 1 + I}, {n, n}];
h = ReplacePart[m[[#]], # -> RandomReal[{-2, 2}, 1][[1]]] & /@ Range@n;
HermitianMatrixQ[h]
h // MatrixForm;

would be welcomed also!