This thesis investigates opinion dynamics on random graphs through the lens of the voter model, a classical interacting particle system used to describe how consensus emerges in networks.

This dissertation presents four separate chapters, all striving towards the same goal: to understand dynamic phenomena occurring in dynamic networks and to explore the emergence of equilibrium in a broad sense.

This dissertation consists of two parts, with the common theme

The parabolic Anderson model (PAM), which is the Cauchy problem for the heat equation with random potential. The PAM is a mathematical model that describes how mass (i.e. matter or energy) flows in a medium in the presence of a field of sources and sinks.

This thesis explores Breaking of Ensemble Equivalence (BEE) in random graph models by examining the spectral properties of adjacency matrices. The goal is to identify spectral characteristics that differentiate random graph ensembles, enhancing the understanding of complex network structures and beh…

This thesis explores Breaking of Ensemble Equivalence (BEE) in random graph models by examining the spectral properties of adjacency matrices. The goal is to identify spectral characteristics that differentiate random graph ensembles, enhancing the understanding of complex network structures and beh…

How do you study the growth of microorganisms, the spread of epidemic diseases or the healing of wounds, without actually performing experiments? Daoyi Wang, PhD candidate at the Mathematical Institute, worked on a specific mathematical model that can describe the growth of microorganisms and many other…