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

Research output: ThesisDissertation (TU Delft)

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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.
Original languageEnglish
QualificationDoctor of Philosophy
Awarding Institution
  • Delft University of Technology
Supervisors/Advisors
  • Redig, F.H.J., Supervisor
  • van Neerven, J.M.A.M., Supervisor
  • Cipriani, A., Advisor
Award date14 Oct 2021
DOIs
Publication statusPublished - 2021

Keywords

  • Interacting particle systems
  • Hydrodynamic limit
  • Equilibrium fluctuations
  • (Discrete) Gaussian Free Field
  • Scaling limit
  • Active particle
  • Riemannian manifold
  • Stochastic processes

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