  We present a method aimed at sampling charge density fluctuations in Coulomb
systems. The derivation follows from a functional integral representation of
the partition function in terms of charge density fluctuations. Starting from
the mean-field solution given by the Poisson-Boltzmann equation, an original
approach is proposed to numerically sample fluctuations around it, through the
propagation of a Langevin like stochastic partial differential equation (SPDE).
The diffusion tensor of the SPDE can be chosen so as to avoid the numerical
complexity linked to long-range Coulomb interactions, effectively rendering the
theory completely local. A finite-volume implementation of the SPDE is
described, and the approach is illustrated with preliminary results on the
study of a system made of two like-charge ions immersed in a bath of
counter-ions.
