Alastair is a second-year Combined Bachelor of Mathematics and Bachelor of Commerce student at the University of Newcastle. He is majoring in Pure Mathematics, Statistics and Finance, and he aims to complete a masters degree in an area which can combine all of these interests. However, he finds it difficult to settle on a choice as studying an area of interest in Mathematics seems to immediately open up five more lines of yet more fascinating query. His hobbies outside of his studies include amateur theatre, music, cycling, and reading.
Random Walks on Derived Graphs
A simple random walk through Zd describes a path taken through a d-dimensional integer lattice, where each of the 2d possible directions is chosen with equal probability. In 1921, George Polya proved that d=1 or d=2 dimensions, such a path will return to its starting position almost surely, but for d = 3 dimensions or higher, the probability of returning to the the starting position decreases as the number of dimensions increases. In this project, we plan to generalise this idea from the integer lattice to more complicated structures through the idea of derived graphs.