Long-time behaviour for discretizations of the Fokker-Planck equation

par Katharina Schuh (TU Wien)

lundi 2 févr. 2026, 15:00 → 16:30 Europe/Paris

112 (Braconnier)

In this talk we construct continuous-time Markov chains associated to finite-volume discretization schemes of Fokker-Planck equations and establish sufficient conditions under which we show quantitative exponential decay in the ϕ-entropy and Wasserstein distance. The decay in ϕ-entropy implies modified logarithmic Sobolev, Poincaré, and discrete Beckner inequalities. The results are not restricted to additive potentials and do not make use of discrete Bochner-type identities. The proof for the ϕ-decay relies on a coupling technique due to Conforti, while the proof for the Wasserstein distance uses the path coupling method. Furthermore, we study an associated discrete-time Markov chain and prove exponential convergence to equilibrium for this chain, based on an abstract discrete Bakry-Emery method and a path coupling. The talk is based on joint work with Ansgar Jüngel (arXiv:2403.10111).