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math.PR2026
A two-scale approach for sampling local free energy minimisers
Antoine Leclerc, Pierre Monmarché
When a free energy admits several local minimisers, the associated mean-field particle system exhibits a metastable behavior, undergoing random transitions between these minimisers…
math.FA2026
Equivalence between -particle log-Sobolev inequalities and non-linear Łojasiewicz inequalities for a class of mean field systems
Pierre Monmarché
The convergence rate of a free energy Wasserstein gradient flow is quantified by its so-called Polyak-Lojasiewicz (PL) constant , which relates the objective function to its dis…
cs.LG2026
Local exponential stability of mean-field Langevin descent-ascent and associated particle system
Geuntaek Seo, Minseop Shin, Pierre Monmarché +1
We study the mean-field Langevin descent-ascent (MFL-DA), a coupled optimization dynamics on the space of probability measures for entropically regularized two-player zero-sum game…