### Anomalous fluctuations of random walks

Probability Seminar

5th May 2023, 3:30 pm – 4:30 pm

Fry Building, 2.04

Understanding the interplay between the geometry of a random space and the stochastic processes that live upon it has been a major focus of probability over the last four decades. In this talk we will focus on the central example of a random walk on a supercritical percolation cluster on the integer lattice. The inhomogeneity of the environment incorporates traps from which the walk will take an anomalously long time to escape. Our main focus will be to discuss how the trapping is exacerbated by adding a bias and understand the different asymptotic behaviours that can arise.

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