Current large deviations of nonreversible diffusions

It is known that calculating means by sampling a Gibbs distribution using Markov chain Monte Carlo algorithms can be made computationally quicker by adding nonreversible transitions or drift terms. In this talk I will give a physical interpretation of this accelerated convergence. Using the level 2.5 of large deviations, accelerated convergence is guaranteed because additional current large deviation costs affect mean fluctuations when compared to the reversible case. I illustrate this general result, and some interesting bounds, for the simple diffusion on the circle and two versions of the Ornstein-Uhlenbeck process in two dimensions.