%0 Generic %1 herzog2017ergodicity %A Herzog, David P. %A Mattingly, Jonathan C. %D 2017 %K Lyapunov %T Ergodicity and Lyapunov functions for Langevin dynamics with singular potentials %U http://arxiv.org/abs/1711.02250 %X We study Langevin dynamics of $N$ particles on $R^d$ interacting through a singular repulsive potential, e.g.~the well-known Lennard-Jones type, and show that the system converges to the unique invariant Gibbs measure exponentially fast in a weighted total variation distance. The proof of the main result relies on an explicit construction of a Lyapunov function. In contrast to previous results for such systems, our result implies geometric convergence to equilibrium starting from an essentially optimal family of initial distributions.

@misc{herzog2017ergodicity, abstract = {We study Langevin dynamics of $N$ particles on $R^d$ interacting through a singular repulsive potential, e.g.~the well-known Lennard-Jones type, and show that the system converges to the unique invariant Gibbs measure exponentially fast in a weighted total variation distance. The proof of the main result relies on an explicit construction of a Lyapunov function. In contrast to previous results for such systems, our result implies geometric convergence to equilibrium starting from an essentially optimal family of initial distributions.}, added-at = {2017-11-08T15:09:50.000+0100}, author = {Herzog, David P. and Mattingly, Jonathan C.}, biburl = {https://www.bibsonomy.org/bibtex/2239dad2b7e7597dc0e55c849fa708c6e/claired}, description = {Ergodicity and Lyapunov functions for Langevin dynamics with singular potentials}, interhash = {5908854516693739818629d6a38338bb}, intrahash = {239dad2b7e7597dc0e55c849fa708c6e}, keywords = {Lyapunov}, note = {cite arxiv:1711.02250}, timestamp = {2017-11-08T15:09:50.000+0100}, title = {Ergodicity and Lyapunov functions for Langevin dynamics with singular potentials}, url = {http://arxiv.org/abs/1711.02250}, year = 2017 }