Uniform-in-time propagation of chaos for singular Lk interaction kernels with rates
Abstract
Based on a semigroup approach, we prove quantitative uniform-in-time propagation of chaos for two systems of interacting particles with singular interaction kernels K of type Lk, k>d, and a contractive Lipschitz confinement force field. First, we consider a system with moderate interaction, which means that the particles interact through the mollified kernel K∗ VN, for some approximation of identity VN = Ndα V(Nα·), α>0. Assuming that |K|Lk is sufficiently small, we obtain that for any ε>0 the uniform-in-time rate is of order N−min(α,1/2−dα/2−ε), plus an exponentially small in time contribution of the initial condition. Second, for the classical, non-mollified particle system we establish uniform-in-time propagation of chaos with rate N−min(α,1/2−dα/2−ε) + |K−K∗ VN|Lk, plus an exponentially small in time contribution of the initial condition. The method relies on the regularity properties of the solution of the associated nonlinear Fokker-Planck equation combined with estimates of the Duhamel formulation of the mollified empirical measure, together with partial Girsanov transforms for the non-mollified system of particles.
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BibTeX
@misc{cazacu2026uniformintime,
title = {{Uniform-in-time propagation of chaos for singular $L^k$ interaction kernels with rates}},
author = {Nicoleta Cazacu and Alexandre Richard and Milica Tomasevic},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15852},
eprint = {2610.15852},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05799936v1},
}
RIS
TY - UNPB
TI - Uniform-in-time propagation of chaos for singular L^k interaction kernels with rates
AU - Nicoleta Cazacu
AU - Alexandre Richard
AU - Milica Tomasevic
PY - 2026
DA - 2026/10/11
PB - HAL
DO - 10.48550/arxiv.2610.15852
UR - https://hal.science/hal-05799936v1
AB - Based on a semigroup approach, we prove quantitative uniform-in-time propagation of chaos for two systems of interacting particles with singular interaction kernels K of type L^k, k>d, and a contractive Lipschitz confinement force field. First, we consider a system with moderate interaction, which means that the particles interact through the mollified kernel K∗ V^N, for some approximation of identity V^N = N^dα V(N^α·), α>0. Assuming that |K|_L^k is sufficiently small, we obtain that for any ε>0 the uniform-in-time rate is of order N^−min(α,1/2−dα/2−ε), plus an exponentially small in time contribution of the initial condition. Second, for the classical, non-mollified particle system we establish uniform-in-time propagation of chaos with rate N^−min(α,1/2−dα/2−ε) + |K−K∗ V^N|_L^k, plus an exponentially small in time contribution of the initial condition. The method relies on the regularity properties of the solution of the associated nonlinear Fokker-Planck equation combined with estimates of the Duhamel formulation of the mollified empirical measure, together with partial Girsanov transforms for the non-mollified system of particles.
ER -