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.
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Room 17, Séminaire "Mathématique Physique"
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Section de mathématiquesIntervenant-e-s
Daniel Ueltschi, University of Warwickentrée libre
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Catégorie: Séminaire