{"paper":{"title":"Geometric Ergodicity of Two--dimensional Hamiltonian systems with a Lennard--Jones--like Repulsive Potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Ben Cooke, David P. Herzog, Jonathan C. Mattingly, Scott A. McKinley, Scott C. Schmidler","submitted_at":"2011-04-19T19:22:46Z","abstract_excerpt":"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. This is a corrected version of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.3842","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}