Advances in Stochastic Duality for Interacting Particle Systems: from many to few

Research output: ThesisDissertation (TU Delft)

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Abstract

Interacting particle systems (IPS) is a subfield of probability theory that provided a fruitful framework in which several questions of physical interests have been answered with mathematical rigor. An interacting particle system is a stochastic system consisting of a very large number of particles interacting with each other. The class of IPS considered in this manuscript is the one of systems satisfying stochastic duality. Stochastic duality is a useful tool in probability theory which allows to study a Markov process (the one that interests you) via another Markov process, called dual process, which is hopefully easier to be studied. The connection between the two processes is established via a function, the so-called duality function, which takes as input configurations of both processes. In the context of IPS, one of the typical simplifications provided by stochastic duality is that a system with an infinite number of particles can be studied via a finite number of particles (the simplification from many to few).
In this thesis, we extend the theory and the applications of stochastic duality in the following two contexts:
i) evolution of particles in space inhomogeneous settings and more precisely, processes in random environment
and processes in a multi-layer system;
ii) evolutions of particles in the continuum.
Original languageEnglish
QualificationDoctor of Philosophy
Awarding Institution
  • Delft University of Technology
Supervisors/Advisors
  • Redig, F.H.J., Supervisor
  • den Hollander, F., Supervisor, External person
  • Giardina, C., Supervisor
Award date28 Oct 2022
DOIs
Publication statusPublished - 2022

Keywords

  • Interacting particle systems
  • Markov Processes
  • Hydrodynamic limit
  • Stochastci Duality
  • Non-equilibrium steady state
  • Random environment
  • Stochastic Homogenization
  • Boundary driven systems
  • Inhomogeneous system

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