Large deviations for mean field particle systems via analysis on spaces of measures
Abstract
This paper introduces a robust strategy to establish large deviation principles for mean field interacting particle systems in T d with vanishing noise. Viewed as a Freidlin-Wentzell type problem, our approach relies on recent techniques for partial differential equations (in short PDE) on the space of probability measures [5]. We first outline the proof strategy for the PDE approach to large deviations in a self-contained manner. As the number of particles goes to infinity, we then show that the transfer function of the system converges to the unique viscosity solution of a limiting Hamilton-Jacobi equation on the space of probability measures. Finally, we explicitly derive the rate function by formulating the solution of this limiting PDE as the value function of an optimal control problem.
Related
- Large spin large deviations for interacting particle systems
- Large Deviations of Invariant Measures of Fractional Reaction-Diffusion Equations Driven by Multiplicative Noise on R^n
- Universal classical and quantum fluctuations in the large deviations of current of noisy quantum systems: Quantum symmetric simple exclusion and inclusion processes
- Large deviations for sparse systems of moving particles
- Tamed Euler Approximation of Invariant Measures for Weakly Interacting Particle Systems and McKean--Vlasov Equations
BibTeX
@misc{pesce2026large,
title = {{Large deviations for mean field particle systems via analysis on spaces of measures}},
author = {Valentin Pesce},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06333},
eprint = {2610.06333},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05774736v1},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Large deviations for mean field particle systems via analysis on spaces of measures
AU - Valentin Pesce
PY - 2026
DA - 2026/10/01
PB - HAL
DO - 10.48550/arxiv.2610.06333
UR - https://hal.science/hal-05774736v1
AB - This paper introduces a robust strategy to establish large deviation principles for mean field interacting particle systems in T d with vanishing noise. Viewed as a Freidlin-Wentzell type problem, our approach relies on recent techniques for partial differential equations (in short PDE) on the space of probability measures [5]. We first outline the proof strategy for the PDE approach to large deviations in a self-contained manner. As the number of particles goes to infinity, we then show that the transfer function of the system converges to the unique viscosity solution of a limiting Hamilton-Jacobi equation on the space of probability measures. Finally, we explicitly derive the rate function by formulating the solution of this limiting PDE as the value function of an optimal control problem.
ER -