Topics in random growth models

: (Alternative Format Thesis)

Abstract

In this thesis we consider the phenomena of coexistence in competing random growth. Our methods rely on the construction of novel mathematical arguments that are able to handle models that lack equilibrium dynamics and monotonicity. Our main contribution is a technique we refer to as multi-scale analysis with non-equilibrium feedback that we believe is a robust method to handle these di cult processes. We apply it to a natural random competition model to deduce a new regime of coexistence on Zd. We also deduce coexistence regimes in other competition models to add to a growing body of literature that analyses interacting particle systems through random growth processes.

Date of Award	13 Dec 2021
Original language	English
Awarding Institution	University of Bath
Supervisor	Alexandre De Oliveira Stauffer (Supervisor)