PreprintCC BY 4.0HAL
Large deviations, gradient flows and fluctuating hydrodynamics for fractional diffusion
Abstract
This work is a step towards a general understanding of fluctuations for systems of particles described at large scale by fractional diffusion. First, we derive formally a Large Deviation Principle for the empirical measure of mean-field interacting particles with a Lévy-type noise. In the case of independent particles, this unveils a generalized gradient flow structure at large scales. Second, we derive and solve numerically a stochastic Partial Differential Equation describing the fluctuating hydrodynamics of this system. The results compare well with direct numerical integration of the particles' dynamics.
Related
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BibTeX
@misc{barre2026large,
title = {{Large deviations, gradient flows and fluctuating hydrodynamics for fractional diffusion}},
author = {Julien Barre and Hiroshi Horii},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18182},
eprint = {2610.18182},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05796131v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Large deviations, gradient flows and fluctuating hydrodynamics for fractional diffusion
AU - Julien Barre
AU - Hiroshi Horii
PY - 2026
DA - 2026/10/12
PB - HAL
DO - 10.48550/arxiv.2610.18182
UR - https://hal.science/hal-05796131v1
AB - This work is a step towards a general understanding of fluctuations for systems of particles described at large scale by fractional diffusion. First, we derive formally a Large Deviation Principle for the empirical measure of mean-field interacting particles with a Lévy-type noise. In the case of independent particles, this unveils a generalized gradient flow structure at large scales. Second, we derive and solve numerically a stochastic Partial Differential Equation describing the fluctuating hydrodynamics of this system. The results compare well with direct numerical integration of the particles' dynamics.
ER -