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Title:
Ergodicity for Langevin dynamics with singular potentials
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Abstract:
We discuss Langevin dynamics of N particles on R^d interacting through a singular repulsive potential, such as the Lennard-Jones potential, and show that the system converges to the unique invariant Gibbs measure exponentially fast in a weighted total variation distance. The proof relies on an explicit construction of a Lyapunov function using a modified Gamma calculus (curvature-dimension condition). In contrast to previous results for such systems, we prove geometric convergence to equilibrium starting from an essentially optimal family of initial distributions. This is based on joint work with F.Baudoin and D.Herzog.
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