Publications [#190155] of Jonathan C. Mattingly

Papers Submitted

1. with Ben Cooke, Scott A. McKinley, Scott C. Schmidler, Geometric Ergodicity of Two--dimensional Hamiltonian systems with a Lennard--Jones--like Repulsive Potential (April, 2011) [math/1104.3842]
   (last updated on 2011/04/22)

   Abstract:
   In this paper we establish the ergodicity of Langevin dynamics for simple two-particle system involving a Lennard-Jones type potential. To the best of our knowledge, this is the first such result for a system operating under this type of potential. Moreover we show that the dynamics are {\it geometrically} ergodic (have a spectral gap) and converge at a geometric rate. Methods from stochastic averaging are used to establish the existence of a Lyapunov function. The existence of a Lyapunov function in this setting seems resistant to more traditional approaches.