<div class="csl-bib-body">
<div class="csl-entry">Schuh, K. J. (2024, June 13). <i>Contractivity for kinetic Fokker-Planck equations with distribution-depedent forces</i> [Conference Presentation]. EQUADIFF Conference 2024, Karlstad, Sweden.</div>
</div>
-
dc.identifier.uri
http://hdl.handle.net/20.500.12708/198616
-
dc.description.abstract
We study the long-time behaviour of the kinetic Fokker-Planck equation by analysing the probabilistic counterpart, the second-order Langevin dynamics. We consider both the classical Langevin dynamics and the nonlinear Langevin dynamics of McKean-Vlasov type containing distribution-dependent forces.
Instead of the classical hypocoercivity methods we use a coupling approach to establish global contraction in an L1 Wasserstein distance with an explicit dimension-free rate for pairwise weak interactions. For external forces corresponding to a κ-strongly convex potential, a contraction rate of order O(√κ) is obtained in certain cases. But the contraction result is not restricted to these forces. It rather includes multi-well potentials and non-gradient-type external forces as well as non-gradient-type repulsive and attractive interaction forces. The proof is based on a novel distance function which combines two contraction results for large and small distances and uses a coupling approach adjusted to the distance. By applying a componentwise adaptation of the coupling we show uniform in time propagation of chaos bounds for the corresponding mean-field particle system.
en
dc.language.iso
en
-
dc.subject
Couplings
en
dc.subject
Langevin dynamics
en
dc.subject
kinetic Fokker-Planck
en
dc.title
Contractivity for kinetic Fokker-Planck equations with distribution-depedent forces
