Large deviations for sparse systems of moving particles
Abstract
We study large deviations for rare clusters in sparse systems of moving particles. In the regime nrnd→0 and ρk,n=nkrnd(k−1)→∞, we prove a large deviation principle for the empirical measure of isolated k-particle trajectory clusters. The speed is ρk,n, and the rate function is the relative entropy h( · |τk), where the finite reference measure τk 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.
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BibTeX
@misc{duan2026large,
title = {{Large deviations for sparse systems of moving particles}},
author = {Cairui Duan and Paula de Dios Andres and Manish Pandey and Miguel A. Ramos Docampo and Brigitte Städler and Christian Hirsch},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.39699},
eprint = {2609.39699},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.39699},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Large deviations for sparse systems of moving particles
AU - Cairui Duan
AU - Paula de Dios Andres
AU - Manish Pandey
AU - Miguel A. Ramos Docampo
AU - Brigitte Städler
AU - Christian Hirsch
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.39699
UR - https://arxiv.org/abs/2609.39699
AB - We study large deviations for rare clusters in sparse systems of moving particles. In the regime nr_n^d→0 and ρ_k,n=n^kr_n^d(k−1)→∞, 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( · |τ_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.
ER -