Uniform long-time and propagation of chaos estimates for mean field kinetic particles in non-convex landscapes

Arnaud Guillin (1) , Pierre Monmarché (2, 3)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal
2 LJLL - Laboratoire Jacques-Louis Lions
3 LCT - Laboratoire de chimie théorique

Combining the results of [14] and [10], the trend to equilibrium in large time is studied for a large particle system associated to a Vlasov-Fokker-Planck equation. Under some conditions (that allow non-convex confining potentials) the convergence rate is proven to be independent from the number of particles. From this are derived uniform in time propagation of chaos estimates and an exponentially fast convergence for the semi-linear equation itself.

Domaines: Probabilités [math.PR]; Equations aux dérivées partielles [math.AP]

Arnaud Guillin, Pierre Monmarché. Uniform long-time and propagation of chaos estimates for mean field kinetic particles in non-convex landscapes. Journal of Statistical Physics, 2021, 185 (2), pp.15. ⟨10.1007/s10955-021-02839-6⟩. ⟨hal-02504451⟩