Finite-Dimensional Approximation in Dual Domain: with Applications in Opinion Dynamics and Dynamic Programming

This thesis is comprised of two main parts. In the first part of the thesis, we study the nonlinear Fokker-Planck (FP) equation that arises as a mean-field (macroscopic) approximation of the bounded confidence opinion dynamics, where opinions are influenced by environmental noises and opinions of radicals (stubborn individuals). The distribution...

Fluctuations for Interacting Particle Systems with Duality

This thesis is concerned with fluctuations of interacting particle systems that<br/>enjoy the property of duality. The main contributions of this work are divided<br/>in two main parts. In the first part we study some of the advantages of looking<br/>at the density fluctuation field through the lenses of orthogonal self-dualities. In<br/>the...

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...