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 socalled 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 multilayer system;
ii) evolutions of particles in the continuum.
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 multilayer system;
ii) evolutions of particles in the continuum.
Original language  English 

Qualification  Doctor of Philosophy 
Awarding Institution 

Supervisors/Advisors 

Award date  28 Oct 2022 
DOIs  
Publication status  Published  2022 
Keywords
 Interacting particle systems
 Markov Processes
 Hydrodynamic limit
 Stochastci Duality
 Nonequilibrium steady state
 Random environment
 Stochastic Homogenization
 Boundary driven systems
 Inhomogeneous system