  We investigate interfacial structural and fluctuation effects occurring at
continuous filling transitions in 3D wedge geometries. We show that
fluctuation-induced wedge covariance relations that have been reported recently
for 2D filling and wetting have mean-field or classical analogues that apply to
higher-dimensional systems. Classical wedge covariance emerges from analysis of
filling in shallow wedges based on a simple interfacial Hamiltonian model and
is supported by detailed numerical investigations of filling within a more
microscopic Landau-like density functional theory. For sufficiently
short-ranged forces mean-field predictions for the filling critical exponents
and covariance are destroyed by pseudo-one-dimensional interfacial
fluctuations. In this filling fluctuation regime we argue that the critical
exponents describing the divergence of lengthscales are related to values of
the interfacial wandering exponent $\zeta(d)$ defined for planar interfaces in
(bulk) two-dimensional ($d=2$) and three-dimensional ($d=3$) systems,
recovering the known results for pure (thermal disorder) systems and predicting
universal critical exponents for the case of random-bond disorder. Finally we
revisit the transfer matrix theory of three-dimensional filling based on an
effective interfacial Hamiltonian model and discuss the interplay between
breather, tilt and torsional interfacial fluctuations.
