Self-repelling walks in dimension d = 2

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This talk will be broadcast at 13:30 GMT January 29th 2024 on MS Teams only.

Meeting ID: 393 527 089 878
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Abstract

As a tourist visiting a new city, you might choose to wander around at random, subject to the constraint that you would rather not visit the same place twice. This behaviour is modelled by the self-repelling random walk, introduced by physicists Amit, Parisi, and Peliti in 1983. We wish to know the large time behaviour of such a walk, but this is difficult to study, in part because the walk is not a Markov process. While a simple random walk is diffusive in every dimension, the self-repelling walk is known to be super-diffusive in dimensions d = 1 and 2. We give a result in dimension d = 2 (the critical dimension) in the so-called weak-coupling regime, and this sheds light on the exact speed of growth.

Joint work with Giuseppe Cannizzaro.

About Harry

Harry is a final year PhD student under the supervision of Dr. Giuseppe Cannizzaro. His interests are in probability and stochastic analysis. He has been working on the question of logarithmic super-diffusivity for the self-repelling Brownian polymer in the critical dimension, d = 2. He is also interested in surface growth models in 2+1 dimensions, such as the dimer model.