Soft-confinement approximation of no-flux McKean-Vlasov dynamics
Abstract
We study the approximation of the no-flux McKean-Vlasov equation on a bounded convex domain by a whole-space equation with quadratic confinement of strength λ−1 outside the domain. For a smooth bounded interaction kernel and a common bounded initial density with square-integrable gradient, we establish an O(λ1/4) approximation rate. The estimate controls the L2 density error uniformly on every finite time interval and the gradient error in space-time L2. Without interaction, a spectral gap independent of λ yields the O(λ1/4) rate uniformly in time for the density error and uniformly over all unit time intervals for the gradient error. With interaction, we construct a counterexample showing that even weak convergence can fail to be uniform in time.
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BibTeX
@misc{seo2026softconfinement,
title = {{Soft-confinement approximation of no-flux McKean-Vlasov dynamics}},
author = {Geuntaek Seo and Yeoneung Kim and Beomjun Choi},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.05431},
eprint = {2611.05431},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.05431},
}
RIS
TY - UNPB
TI - Soft-confinement approximation of no-flux McKean-Vlasov dynamics
AU - Geuntaek Seo
AU - Yeoneung Kim
AU - Beomjun Choi
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.05431
UR - https://arxiv.org/abs/2611.05431
AB - We study the approximation of the no-flux McKean-Vlasov equation on a bounded convex domain by a whole-space equation with quadratic confinement of strength λ^−1 outside the domain. For a smooth bounded interaction kernel and a common bounded initial density with square-integrable gradient, we establish an O(λ^1/4) approximation rate. The estimate controls the L^2 density error uniformly on every finite time interval and the gradient error in space-time L^2. Without interaction, a spectral gap independent of λ yields the O(λ^1/4) rate uniformly in time for the density error and uniformly over all unit time intervals for the gradient error. With interaction, we construct a counterexample showing that even weak convergence can fail to be uniform in time.
ER -