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SUMMARY:Spatial shuffling: the interchange process in dimension 5 - Allan 
 Sly (Princeton)
DTSTART:20241104T170000Z
DTEND:20241104T180000Z
UID:TALK218443@talks.cam.ac.uk
CONTACT:Professor Ioannis Kontoyiannis
DESCRIPTION:The interchange process $\\sigma_T$ is a random permutation va
 lued stochastic process on a graph evolving in time by transpositions on i
 ts edges at rate 1. On $Z^d$\, when $T$ is small all the cycles of the per
 mutation $\\sigma_T$ are finite almost surely but it is conjectured that i
 nfinite 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 macro
 scopic cycles with Poisson-Dirichlet statistics appear for large times in 
 dimensions 5 and above.\n\nA wine reception in the Central Core will follo
 w the talk.  \nAll welcome  \n\nA recording of this talk can be found "her
 e":https://www.youtube.com/watch?v=28p6CAiSjYQ&t=41s
LOCATION:MR2\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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