Linear charged particle simulations

Today's paper is by Joerg Rottler and A.C. Maggs, entitled "A Continuum,O(N) Monte-Carlo algorithm for charged particles". There are some earlier papers in the references where this method was developed for lattice systems.

As near as I can tell, the algorithm works by writing the total energy in terms of the electric field rather than the electric potential. The electric field is put on a grid. Particle moves then only require local updates to the electric field grid.

The electrostatic interaction is generated as a result of minimizing the energy functional (functional of the electric field). The algorithm they give is supposed to recover the proper interaction by a Monte Carlo means. This is the part I don't quite understand yet.

It seems like a good example of exploiting Monte Carlo to reduce the complexity of a problem by solving it on average.