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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.20167 |
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| _version_ | 1866911593271394304 |
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| author | Junné, Jonathan Redig, Frank Versendaal, Rik |
| author_facet | Junné, Jonathan Redig, Frank Versendaal, Rik |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_20167 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hydrodynamic limit of the symmetric exclusion process on complete Riemannian manifolds and principal bundles Junné, Jonathan Redig, Frank Versendaal, Rik Probability 58J65, 60D05, 60K37, 82B43 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. |
| title | Hydrodynamic limit of the symmetric exclusion process on complete Riemannian manifolds and principal bundles |
| topic | Probability 58J65, 60D05, 60K37, 82B43 |
| url | https://arxiv.org/abs/2410.20167 |