Student Probability and Mathematical Physics Seminar

In this talk I will discuss the approaches for proving convergence of the overdamped Langevin Monte Carlo scheme. The two most well-established approaches are via coupling and via Fokker-Planck equations and stability estimates. I will start by reviewing the classical coupling argument for 2-Wasserstein convergence, and compare it to the Fokker-Planck approach. Then, I will present a recent result on the convergence of low-dimensional marginal distributions using a Fokker-Planck argument and a hierarchical entropy construction. If time permits, I will go through a coupling argument for the same result. Referneces: Vempala and Wibisono (2019), Lacker and Zhou (2025), Chen, Cheng, Niles-Weed, and Weare (2025).