Symmetric interacting particle systems

Self-duality and hydrodynamics in dynamic random environment

Doctoral thesis (2019)

Authors

F. Sau Applied Probability - EEMCS
Research Group
Applied Probability (EEMCS) (TU Delft)
Copyright: © 2019 F. Sau
DOI
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https://doi.org/10.4233/uuid:a0b4bc54-ec9b-4eb7-92d2-6a751993e5d9
Duality Markov processes Hydrodynamics Interacting particle systems Random walks
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Published Date

2019

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 scaling and detailed properties of a class of conservative interacting particle systems. In particular, in the first part we derive the hydrodynamic equation for the symmetric exclusion process in presence of dynamic random environment. The second part of the thesis focuses on a detailed property of conservative particle systems and, more generally, of Markov processes, called duality. There, we study and characterize duality and self-duality relations for so-called symmetric interacting particle systems.