Some Remarks on Preconditioning Molecular Dynamics

Overview & Synopsis

We consider a Preconditioned Overdamped Langevin algorithm that does not alter the invariant distribution (up to controllable discretisation errors) and ask whether precondi-tioning improves the standard model in terms of reducing the asymptotic variance and of accelerating convergence to equilibrium. We present a detailed study of the dependence of the asymptotic variance on preconditioning in some elementary toy models related to molecular simulation. Our theoretical results are supported by numerical simulations.