Modelling bivariate exposure distributions for Out of Home advertising

Out of Home advertising is traditional outdoor advertising. Over the last decade the digital Out of Home advertising possibilities have grown substantially. These possibilities include hour-based advertisement schedules, rapidly implemented changes to advertisements and obtaining location data from consumers being exposed to advertisements....

Criticality in the Abelian sandpile model

In this thesis we study criticality in the context of the dissipative Abelian sandpile model. The model is linked to a simple trapped random walk, giving a practical method to determine criticality for certain landscapes of dissipative sites. The main results concern the lifetime of the random walk, especially the divergence of its first moment...

Dissipation in the Abelian sandpile model: Conditions for criticality

The Abelian sandpile model was first introduced by Bak, Tang and Wiesenfeld in 1987. Since then, a lot of researchers have studied this model and similar models, all related by the concept of self-organized criticality. In this thesis, we study a variant on the classical model where dissipative and anti-dissipative vertices are incorporated in...

On different characterizations of a normal distribution

The normal distribution is a very important distribution in probability theory and statisticsand has a lot of unique properties and characterizations. In this report we look at the proof of two of these characterizations and create counterparts of a normal distribution on abstract spaces, such as vector spaces and groups, which we shall call...

Brownian Motion and the Airy Function

Deriving the location of the maximum of a Brownian Motion with downward quadratic drift. Proving it is welldefined then finding an algorithmic method to simplify expressions of the moments.