Stochastic diffusions for sampling Gibbs measures

I will discuss properties of stochastic differential equations and numerical algorithms for sampling Gibbs (i.e smooth) measures. Methods such as Langevin dynamics are reliable and well-studied performers for molecular sampling. I will show that, when the objective of simulation is sampling of the configurational distribution, it is possible to obtain a superconvergence result (an unexpected increase in order of accuracy) for the invariant distribution. I will also describe an application of thermostats to the Hamiltonian vortex method in which the energetic interactions with a bath of weak vortices are treated as thermal fluctuations.