具有奇异势和乘性噪声的Langevin相互作用系统的 Ergodicity 与渐近极限
概率论
2026-02-27 v3 数学物理
动力系统
math.MP
摘要
本文研究由奇异势和乘性噪声描述的N个相互作用粒子系统，包括经典和相对Langevin动力学。对于经典模型，我们证明了其ergodicity，得到对不变布尔- Gibbs分布指数级收敛速率，并得到小质量极限，恢复N粒子相互作用的过阻尼Langevin动力学。对于相对模型，我们建立了ergodicity，得到任意阶的Maxwell-J"uttner分布代数混合速率，并得到牛顿极限（即光速趋于无穷），近似Underdamped Langevin动力学系统。证明依赖于考虑不规则势和乘性噪声的Lyapunov函数构造。
引用
@article{arxiv.2601.04974,
title = {Ergodicity and asymptotic limits for Langevin interacting systems with singular forces and multiplicative noises},
author = {Manh Hong Duong and Hung Dang Nguyen and Wenxuan Tao},
journal= {arXiv preprint arXiv:2601.04974},
year = {2026}
}
备注
Version 2 was uploaded in error and contained an unrelated manuscript. Version 3 restores the correct paper