  We show that the refined Donaldson-Thomas invariants of C3, suitably
normalized, have a Gaussian distribution as limit law. Combinatorially these
numbers are given by weighted counts of 3D partitions. Our technique is to use
the Hardy-Littlewood circle method to analyze the bivariate asymptotics of a
q-deformation of MacMahon's function. The proof is based on that of E.M. Wright
who explored the single variable case.
