Properties of Random Walks and their applications to Mathematical Physics

The project is devoted to the study of the time that simple random walk on 𝑍^𝑑 visits each
vertex. This is called local time profile, and it is pivotal in the study of processes obtained
by a change of measure of simple random walks, which we call “polymer measure”. Our
goal is to analyse localization of polymer measures. In particular we, review some old and
new results about polymers obtained by penalizing the paths of simple random walk by
their range. These “new” paths obey a shape theorem, i.e. the range will resemble balls in
𝑍^𝑑 of radius 𝑁^1/(𝑑+2) where 𝑁 is the time horizon.

Liam Wood-Baker

Monash University

Liam Wood-Baker is an undergraduate student at Monash University. He is currently studying for a Bachelor of Science / Bachelor of Arts double degree, with majors in Mathematics and Chinese. In Mathematics, he has found himself particularly interested in Analysis and Statistics. He is also interested in Computer Science, and applications of Mathematics to Computer Science. As such, he has completed a Minor in Computational Science as part of his degree.

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