<div class="csl-bib-body">
<div class="csl-entry">Schuh, K. J. (2024, September 18). <i>Global contractivity for Langevin dynamics with distribution-dependent forces via couplings</i> [Conference Presentation]. Large scale behaviour of interacting diffusions, Italy.</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/201163
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dc.description.abstract
We analyse the long-time behaviour of both the classical second-order Langevin dynamics and the nonlinear second-order Langevin dynamics of McKean-Vlasov type. After giving a short recap on coupling methods we introduce 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 aκ-strongly convex potential, a contraction rate of order O(√k) is obtained in certain cases. But, the contraction result is not restricted to these external 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 construction adjusted to the distance. By applying a componentwise adaptation of the coupling we can prove uniform in time propagation of chaos bounds for the corresponding mean-field particle system.
en
dc.language.iso
en
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dc.subject
Langevin dynamics
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dc.subject
couplings
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dc.subject
long-time behaviour
en
dc.title
Global contractivity for Langevin dynamics with distribution-dependent forces via couplings
