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Directed Spatial Permutations on Asymmetric Tori
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
Venue:
Mathematical Institute, Woodstock Road OX2 6GG
Venue 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
