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arXiv · 2610.18182

Large deviations, gradient flows and fluctuating hydrodynamics for fractional diffusion

Julien Barre·Hiroshi Horii
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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 L{é}vy-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.

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Julien Barre, Hiroshi Horii. 2026-10-13. Large deviations, gradient flows and fluctuating hydrodynamics for fractional diffusion. https://arxiv.org/abs/2610.18182

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