{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/ergodicity-of-langevin-dynamics-and-its","title":"Ergodicity of Langevin Dynamics and its Discretizations for Non-smooth Potentials","arxiv_id":"2411.12051","date":"2024-11-18","proceeding":null,"authors":["Lorenz Fruehwirth","Andreas Habring"],"abstract":"This article is concerned with sampling from Gibbs distributions $\\pi(x)\\propto e^{-U(x)}$ using Markov chain Monte Carlo methods. In particular, we investigate Langevin dynamics in the continuous- and the discrete-time setting for such distributions with potentials $U(x)$ which are strongly-convex but possibly non-differentiable. We show that the corresponding subgradient Langevin dynamics are exponentially ergodic to the target density $\\pi$ in the continuous setting and that certain explicit as well as semi-implicit discretizations are geometrically ergodic and approximate $\\pi$ for vanishing discretization step size. Moreover, we prove that the discrete schemes satisfy the law of large numbers allowing to use consecutive iterates of a Markov chain in order to compute statistics of the stationary distribution posing a significant reduction of computational complexity in practice. Numerical experiments are provided confirming the theoretical findings and showcasing the practical relevance of the proposed methods in imaging applications.","url_abs":"https://arxiv.org/abs/2411.12051v1","url_pdf":"https://arxiv.org/pdf/2411.12051v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"ergodicity-of-langevin-dynamics-and-its","repo_url":"https://github.com/habring/ergodicity_subgradient_langevin","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2411.12051","atlas_url":"https://app.syntology.ai/?focus=2411.12051","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}