Print Email Facebook Twitter Advances in Stochastic Duality for Interacting Particle Systems: from many to few Title Advances in Stochastic Duality for Interacting Particle Systems: from many to few Author Floreani, S. (TU Delft Applied Probability) Contributor Redig, F.H.J. (promotor) den Hollander, F. (promotor) Giardina', C. (promotor) Degree granting institution Delft University of Technology Date 2022-10-28 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 environmentand processes in a multi-layer system;ii) evolutions of particles in the continuum. Subject Interacting particle systemsMarkov ProcessesHydrodynamic limitStochastci DualityNon-equilibrium steady stateRandom environmentStochastic HomogenizationBoundary driven systemsInhomogeneous system To reference this document use: https://doi.org/10.4233/uuid:1d06f2e4-ec60-47f8-aed8-e8ca21f1fffe Part of collection Institutional Repository Document type doctoral thesis Rights © 2022 S. Floreani Files PDF main.pdf 2.8 MB Close viewer /islandora/object/uuid:1d06f2e4-ec60-47f8-aed8-e8ca21f1fffe/datastream/OBJ/view