Hydrodynamic limit of the symmetric exclusion process on a compact Riemannian manifold. (English) Zbl 1435.82021
Summary: We consider the symmetric exclusion process on suitable random grids that approximate a compact Riemannian manifold. We prove that a class of random walks on these random grids converge to Brownian motion on the manifold. We then consider the empirical density field of the symmetric exclusion process and prove that it converges to the solution of the heat equation on the manifold.
MSC:
| 82C22 | Interacting particle systems in time-dependent statistical mechanics |
| 82C41 | Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics |
| 60J65 | Brownian motion |
| 58J60 | Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) |
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