We will be interested in stochastic dynamics on high-dimensional energy landscapes which are metastable. This means that the dynamics remains trapped for very long period of times in some subdomains of the configurational space (called metastable states). Such dynamics are typically used to describe the evolution of a molecular system at a fixed temperature, and the metastable states then correspond to molecular conformations which are successively visited, as the dynamics go frome one metastable state to another. There are at least two questions of interest in this context: (i) What are the typical paths which are followed by the dynamics to go from one metastable state to another ? (ii) Is it possible to accurately approximate the dynamics with some kind of jump process, which would only reproduce the jumps among the metastable states. In the context of molecular simulation, the first question is related to the description of transition and reactive paths ; the second one is connected to the study of the rigorous foundations of Markov state models and kinetic Monte Carlo models. We will present algorithms and mathematical analysis which have been devised to address these questions, and in particular splitting techniques and accelerated molecular dynamics methods.
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