  We investigate the matching of eigenvalue densities of Wilson loops in SU(N)
lattice gauge theory: the eigenvalue densities in 1+1, 2+1 and 3+1 dimensions
are nearly identical when the traces of the loops are equal. We show that the
matching is present to at least second order in the strong-coupling expansion,
and also to second order in perturbation theory. We find that in the continuum
limit there is matching at all values of the trace for bare Wilson loops. We
confirm numerically that there is matching in these limits and find there are
small violations away from them. We discuss the implications for the bulk
transitions and for non-analytic gap formation at N = infinity in 2+1 and 3+1
dimensions.
