Discipline: 
Mathematics
Status: 
Available
Level: 
PhD Project
Level: 
Masters Project
Supervisor(s): 
Dr Thomas Taimre

Many networks from crystalline lattices to social networks display so-called self-organizing phenomena. This essentially means that global order or chaos can emerge from simple local rules.  Particular interest has been paid to these phenomena in light of residential segregation in the US by race and papers by Schelling predicting that such phenomena can arise with remarkably low levels of racial intolerance. Such predictions are normally confined to unrealistic models such as that the city or crystal is on a rectangular lattice. 

In this project you will investigate self-organizing networks in a broad sense and consider simple extensions of the basic models to consider networks where the underlying structure changes as well as individuals or particles move. Background in probability theory is preferred.