  We investigate the dependence of the Yang-Mills wave functional in Coulomb
gauge on the Faddeev-Popov determinant. We use a Gaussian wave functional
multiplied by an arbitrary power of the Faddeev-Popov determinant. We show,
that within the resummation of one-loop diagrams the stationary vacuum energy
is independent of the power of the Faddeev-Popov determinant and, furthermore,
the wave functional becomes field-independent in the infrared, describing a
stochastic vacuum. Our investigations show, that the infrared limit is rather
robust against details of the variational ans\"atze for the Yang-Mills wave
functional. The infrared limit is exclusively determined by the divergence of
the Faddeev-Popov determinant at the Gribov horizon.
