  We show that information on the probability density of local fluctuations can
be obtained from a numerical renormalisation group calculation of a reduced
density matrix. We apply this approach to the Anderson-Holstein impurity model
to calculate the ground state probability density $\rho(x)$ for the
displacement $x$ of the local oscillator. From this density we can deduce an
effective local potential for the oscillator and compare its form with that
obtained from a semiclassical approximation as a function of the coupling
strength. The method is extended to infinite dimensional Holstein-Hubbard model
using dynamical mean field theory. We use this approach to compare the
probability densities for the displacement of the local oscillator in the
normal, antiferromagnetic and charge ordered phases.
