Random permutations show up in a variety of areas in mathematics and its applications. In connection with physical applications (e.g., the lambda transition for superfluid helium), there is an interest in random spatial permutations — that is, laws on permutations that have a ‘geometric bias’. There are compelling heuristic arguments that this spatial bias has little effect on the distribution of the largest cycles of a random spatial permutation, provided that large cycles actually exist. I’ll discuss a particular model of random spatial permutations (directed permutations on asymmetric tori) where these heuristics can be made precise, and large cycles can be shown to follow the expected (Poisson-Dirichlet) law.

Based on joint work with Alan Hammond.

**Date**: 31 May 2023, 11:00 (Wednesday, 6th week, Trinity 2023)**Venue**: Mathematical Institute

Woodstock Road OX2 6GGSee location on maps.ox**Details**: L4**Speaker**: Tyler Helmuth (Durham University)**Organising department**: Department of Statistics**Part of**: Probability seminar**Booking required?**: Not required**Audience**: Public- Editors: Christina Goldschmidt, James Martin, Julien Berestycki