Hydrodynamic Limit of the Symmetric Exclusion Process on a Compact Riemannian Manifold

Journal article (2019)

Authors

G.J. van Ginkel Applied Probability - EEMCS
F.H.J. Redig Applied Probability - EEMCS
Research Group
Applied Probability (EEMCS) (TU Delft)
Copyright: © 2019 G.J. van Ginkel, F.H.J. Redig
DOI: https://doi.org/10.1007/s10955-019-02420-2
More Info
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Published Date

2019

Language

English

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Applied Probability

Abstract

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.