Symmetric interacting particle systems: Self-duality and hydrodynamics in dynamic random environment

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...

Factorized Duality, Stationary Product Measures and Generating Functions

We find all self-duality functions of the form (Formula presented.)for a class of interacting particle systems. We call these duality functions of simple factorized form. The functions we recover are self-duality functions for interacting particle systems such as zero-range processes, symmetric inclusion and exclusion processes, as well as...

Duality and Stationary Distributions of the “Immediate Exchange Model” and Its Generalizations

We study the “Immediate Exchange Model”, a wealth distribution model introduced in Heinsalu and Patriarca (Eur Phys J B 87:170, 2014). We prove that the model has a discrete dual, where the duality functions are natural polynomials associated to the Gamma distribution with shape parameter 2 and are exactly those connecting the Brownian Energy...