  We present a simple and systematic procedure to determine the effective
dynamics of a Brownian particle coupled to a rapidly fluctuating correlated
medium, modeled as a scalar Gaussian field, under spatial confinement. The
method allows us, in particular, to address the case in which the fluctuations
of the medium are suppressed in the vicinity of the particle, as described by a
quadratic coupling in the underlying Hamiltonian. As a consequence of the
confinement of the correlated medium, the resulting effective Fokker-Planck
equation features spatially dependent drift and diffusion coefficients. We
apply our method to simplified fluid models of binary mixtures and
microemulsions near criticality containing a colloidal particle, and we analyze
the corrections to the stationary distribution of the particle position and the
diffusion coefficient.
