A brief introduction into the lattice Boltzmann method is given. For
soft-matter applications, it is necessary to include thermal
fluctuations by introducing stochastic collision rules. This can be
done consistently based upon the concept of detailed balance.
Brownian particles are coupled to the lattice Boltzmann solvent
via a Stokes friction and interpolation. The Langevin equations
of the overall system satisfy both momentum conservation and
the fluctuation-dissipation theorem. The long-time mobility of the