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Gabriel Stoltz : Langevin dynamics at equilibrium and out of equilibrium: from hypocoercivity to efficient sampling

I will present various results on the Langevin dynamics, both from theoretical and numerical perspectives. This dynamics is quite popular for sampling purposes in computational statistical physics. It can be seen as a Hamiltonian dynamics perturbed by an Ornstein-Uhlenbeck process on the momenta. I will start on the theoretical side with an account of the hypocoercive approach by Dolbeault, Mouhot and Schmeiser, which is a key technique to prove that the asymptotic variance of time averages is well defined, and also to obtain quantitative bounds on it. I will then discuss various extensions/modifications of the standard Langevin dynamics, such as replacing the standard quadratic kinetic energy by a more general one, constructing control variates relying on a simplified Poisson equation, proving the convergence of nonequilibrium versions such as the one encountered in the Temperature Accelerated Molecular Dynamics method, etc.

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