Correlated Brownian motions and the depletion effect in colloids

We briefly review the derivation of a system of N correlated Brownian motions as a kinematic mesoscopic limit for a system of nonlinear deterministic oscillators consisting of N large (solute) particles and infinitely many small (solvent) particles by Kotelenez. We then sketch the qualitative analysis of correlated Brownian motions and the depletion effect in colloids by Kotelenez, Leitman and Mann. For space dimension d >= 2 they showed that two correlated Brownian particles, when sufficiently close, have an initial tendency to attract each other further. For large times (and for large separations) they perform independent Brownian motions. The key to their short-time result is a generalization to d >= 2 dimensions of the one-dimensional probability flux, as defined by van Kampen. We conclude with a discussion of three unresolved problems.