The Symmetric Exclusion Process and the Gausian Free Field on compact Riemannian manifolds

Doctoral thesis (2021)

Authors

G.J. van Ginkel Applied Probability - EEMCS
Research Group
Applied Probability (EEMCS) (TU Delft)
Copyright: © 2021 G.J. van Ginkel
DOI: https://doi.org/10.4233/uuid:0a0344dc-b98b-4539-8456-2c6de4843315
Hydrodynamic limit Interacting particle systems Equilibrium fluctuations (Discrete) Gaussian Free Field Scaling limit Active particle Riemannian manifold Stochastic processes
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Published Date

2021

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Applied Probability

Abstract

In this thesis we study the Symmetric Exclusion Process (SEP) and the Discrete Gaussian Free Field (DGFF) on compact Riemannian manifolds. In particular, we obtain the hydrodynamic limit and the equilibrium fluctuations of SEP and we show that the DGFF converges to its continuous counterpart. To define these discrete models, we construct grids with edge weights that approximate the underlying manifold in a suitable way. Additionally, we study a model of an active particle and the role of reversibility for its limiting diffusion coeffcient and large deviations rate function.