发表机构
Aarhus University（奥胡斯大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究移动粒子稀疏系统中罕见簇的大偏差，证明了孤立k粒子轨迹簇经验测度的大偏差原理，推导了自由能变分公式，并应用于磁性微电机轨迹建模。
AI 中文摘要
我们研究了移动粒子稀疏系统中罕见簇的大偏差。在区域\\(nr_n^d\to0\\)且\\(\rho_{k,n}=n^kr_n^{d(k-1)}\to\infty\\)的范围内，我们证明了孤立\\(k\\)-粒子轨迹簇的经验测度的大偏差原理。速度为\\(\rho_{k,n}\\)，速率函数是相对熵\\(h(\\,\cdot\mid\tau_k)\\)，其中有限参考测度\\(\tau_k\\)明确包含了潜在的路径定律。作为推论，我们推导了有界相互作用和硬核约束的自由能变分公式，并确定了相应的最小化簇定律。归一化的优化器为相互作用轨迹簇的Metropolis--Hastings采样提供了基础。作为由活性粒子系统中链形成和群集现象所启发的应用，我们将所得随机模型校准到磁性微电机的实验轨迹，发现拟合的速度尺度随粒子尺寸和磁力系统地变化。
英文摘要
We study large deviations for rare clusters in sparse systems of moving particles. In the regime \(nr_n^d\to0\) and \(ρ_{k,n}=n^kr_n^{d(k-1)}\to\infty\), we prove a large deviation principle for the empirical measure of isolated \(k\)-particle trajectory clusters. The speed is \(ρ_{k,n}\), and the rate function is the relative entropy \(h(\,\cdot\,\midτ_k)\), where the finite reference measure \(τ_k\) explicitly incorporates the underlying path law. As consequences, we derive free-energy variational formulas for bounded interactions and a hard-core constraint and identify the corresponding minimizing cluster law. The normalized optimizer provides the basis for Metropolis--Hastings sampling of interacting trajectory clusters. As an application motivated by chain formation and swarming in active particle systems, we calibrate the resulting stochastic model to experimental trajectories of magnetic micromotors and find that the fitted velocity scale varies systematically with particle size and magnetic forcing.
