School of Mathematical Sciences

Random interchange model on the complete graph and the Poisson-Dirichlet distribution menu

Random interchange model on the complete graph and the Poisson-Dirichlet distribution

Speaker: 
Daniel Ueltschi (Warwick)
Date/Time: 
Wed, 11/10/2017 - 13:00
Room: 
Queen's Building, W316

In 2005, Schramm considered the random interchange model on the complete graph and he proved
that the lengths of long cycles have Poisson-Dirichlet distribution PD(1). If one adds the weight
2^{#cycles}, one gets Tóth’s representation of the quantum Heisenberg model. In this case, we
prove (essentially) that long cycles have distribution PD(2). In a related model of random loops,
that involves “double bars” as well as “crosses”, we prove that long loops have distribution PD(1).
Joint work with J. Björnberg and J. Fröhlich.