The Langevin dynamics are widely used in computational statistical physics to model the evolution of a molecular system. In many situations of interest, the process is metastable, meaning that it remains trapped in a so-called metastable domain for very long times. In such a case, it is expected that the process reaches a local equilibrium distribution within the metastable domain before leaving it. This distribution is called the quasi-stationary distribution (QSD). Proving the existence of this limiting behavior is in particular important to prove the consistency of accelerated dynamics algorithms, e.g. the parallel replica method. We shall present in this talk recent results related to this question.

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