Hydrodynamic limit of the symmetric exclusion process on complete Riemannian manifolds and principal bundles

2024/10/26 by Jonathan Junné, Junné, Jonathan, Frank Redig +3
Mathematics · Physics and Astronomy · #58J65 #60D05 #60K37 #82B43 #Cosmology and Gravitation Theories #FOS: Mathematics #Geometric Analysis and Curvature Flows #Probability (math.PR) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2410.20167

openalex publication_date 2024/10/26 · openalex created_date 2024/11/14 · openalex updated_date 2026/07/28

Abstract

We prove that the hydrodynamic limit of the symmetric exclusion process (SEP) is a Fokker-Planck equation in the setting of Poisson random neighborhood graphs approximating a weighted Riemannian manifold with Ricci curvature bounded from below. We also consider the lift of the SEP to a principal bundle, and obtain a Fokker-Planck equation with a weighted horizontal Laplacian as its hydrodynamic limit. Both results significantly extend the geometric settings in which one can prove the hydrodynamic limit from duality combined with convergence of the single particle random walk towards a diffusion process.

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