Pawel graduated from the University of Durham with an MMath in 2020 where his main interest was probability theory and statistics. For his final year project, he studied the discrete percolation; in particular, he investigated various methods to obtain bounds for critical probabilities. He is now looking forward to exploring more about random walks and random environment. Apart from Maths, he enjoys playing volleyball, cooking and he loves to learnabout the British royal family.

Research project title:
Once-reinforced random walks on tree-like graphs

Supervisor(s):
Daniel Kious, Hendrik Weber

Project description:
Once reinforced random walk (ORRW) is an example of a self-interacting random walk, which is not Markovian, and hence, the study of it often proves to be rather nontrivial. It has been studied mainly on trees, and the existence of a phase transition for recurrence/transience has been established on those graphs. There have only been a few results obtained for ORRW on non-simple graphs, exclusively on ‘ladder graphs’, which are essentially one-dimensional. Pawel is investigating ORRW on tree-like graphs, that is, graphs with loops which additionally possess a useful tree structure. In particular, Pawel’s research concerns learning about the phase transition on that class of graphs.