Dynamics of random graphs and interacting particle systems

Abstract

The talk will be based on the thesis which has broadly two objectives. In the first part of the thesis we study a certain random dynamics of discrete sparse graphs on n vertices(based on the Moran model) and understand the limit as n goes to infinity. In the second part of the thesis we provide a trajectorial representation for a semi linear parabolic partial differential equation. In this talk we will mainly focus on the results concerning the dynamics of sparse graphs. We will begin with the preliminaries of the sparse graphs and convergences. Following which we will define the Moran model and its scaling limit, namely Wright-Fisher diffusion. We will use these to construct random dynamics of discrete sparse graphs on n vertices and study the limit as n goes to infinity.