Sampling normalizing constants in high dimensions using inhomogeneous diffusions

Motivated by the task of computing normalizing constants and importance sampling in high dimensions, we study,in this paper, the dimension dependence of fluctuations for additive functionals of time-inhomogeneous Langevin-type diffusions on $\ mathbb {R}^{d} $. The main results are nonasymptotic variance and bias bounds. I will discuss in this talk the main tools and motivation that allow us to arrive to those results.