Spatial shuffling: the interchange process in dimension 5

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• Allan Sly (Princeton)
• Monday 04 November 2024, 17:00-18:00
• MR2, CMS, Wilberforce Road, Cambridge, CB3 0WB.

If you have a question about this talk, please contact Professor Ioannis Kontoyiannis.

The interchange process $\sigma_T$ is a random permutation valued stochastic process on a graph evolving in time by transpositions on its edges at rate 1. On $Z^d$, when $T$ is small all the cycles of the permutation $\sigma_T$ are finite almost surely but it is conjectured that infinite cycles appear in dimensions 3 and higher for large times. In this talk I will focus on the finite volume case where we establish that macroscopic cycles with Poisson-Dirichlet statistics appear for large times in dimensions 5 and above.

A wine reception in the Central Core will follow the talk. All welcome

A recording of this talk can be found here

This talk is part of the Rollo Davidson Lectures series.

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