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We consider a one-dimensional McKean-Vlasov SDE on a domain and theassociated mean-field interacting particle system. The peculiarity of thissystem is the combination of the interaction, which keeps the average positionprescribed, and the reflection at the boundaries; these two factors make theeffect of reflection non local. We show pathwise well-posedness for theMcKean-Vlasov SDE and convergence for the particle system in the limit of largeparticle number.

A McKean-Vlasov SDE and particle system with interaction from reflecting boundaries