Random interchange model on the complete graph and the Poisson-Dirichlet distribution (Daniel Ueltschi, University of Warwick)

18.12.2017 15:15

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 Toth'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. Bjornberg and J. Frohlich.

Lieu

Room 17, Séminaire "Mathématique Physique"

Organisé par

Section de mathématiques

Intervenant-e-s

Daniel Ueltschi, University of Warwick

entrée libre

Classement

Catégorie: Séminaire