| Popis: |
The topic of this thesis is random growth processes. These occur naturally in many real world settings such as in the growth of tumours and lightning strikes. As such we would like to model the processes so that we can effectively study their properties. In particular, we are interested in what the shape of the process is as it grows and so we wish to evaluate the scaling limits of the random processes. In Chapter 1, we will provide the background material needed in order to study the random growth models. We will give examples of real world processes that we would like to study before describing the models used to study them. We then provide some previous results in the area to provide context for the independent research that follows. Chapter 2 will follow [LT21a] closely. In this paper we evaluate a strongly regularised version of the Hastings-Levitov model HL(α) for 0≤α |
