Freidlin-Wentzell collision-laws between self-stabilizing diffusions
Abstract
The present work investigates the asymptotic behaviours at the zero-noise limit of the first near collision-time and first near collision-location between a pair of independent d-dimensional Brownian-driven self-stabilizing (McKean-Vlasov type) diffusions. These asymptotic are considered in a peculiar setting where the systems evolve in a bi-stable landscape and collisions are only triggered by the combined action of the Brownian noises. As the Brownian perturbations fade away, we show that the near collision-time increases at an explicit exponential rate and that related collision-locations persist in specific regions of the space. These results are mainly derived by tailoring classical Freidlin-Wentzell's exit-time (and exit-location) estimates into collision estimates. Similar asymptotic are established for related mean-field interacting particle system approximation, and for the one-dimensional case (where true collisions can be examined
Related
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- Propagation Dynamics for Multidimensional Nonlocal Diffusion Equations: A General Freidlin-Gärtner Formula
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BibTeX
@misc{jabir2026freidlinwentzell,
title = {{Freidlin-Wentzell collision-laws between self-stabilizing diffusions}},
author = {Jean-François Jabir and Julian Tugaut},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.27932},
eprint = {2607.27932},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.27932},
}
RIS
TY - UNPB
TI - Freidlin-Wentzell collision-laws between self-stabilizing diffusions
AU - Jean-François Jabir
AU - Julian Tugaut
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2607.27932
UR - https://arxiv.org/abs/2607.27932
AB - The present work investigates the asymptotic behaviours at the zero-noise limit of the first near collision-time and first near collision-location between a pair of independent d-dimensional Brownian-driven self-stabilizing (McKean-Vlasov type) diffusions. These asymptotic are considered in a peculiar setting where the systems evolve in a bi-stable landscape and collisions are only triggered by the combined action of the Brownian noises. As the Brownian perturbations fade away, we show that the near collision-time increases at an explicit exponential rate and that related collision-locations persist in specific regions of the space. These results are mainly derived by tailoring classical Freidlin-Wentzell's exit-time (and exit-location) estimates into collision estimates. Similar asymptotic are established for related mean-field interacting particle system approximation, and for the one-dimensional case (where true collisions can be examined
ER -