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Séminaire de probabilités et physique statistique de l'IHES

Universality of fluctuation of the dimer model

by Prof. Gourab Ray (Victoria University & IHES)

mardi 31 octobre 2017 de au (Europe/Paris)
at IHES ( Amphithéâtre Léon Motchane )
Le Bois-Marie 35, route de Chartres 91440 Bures-sur-Yvette
Description

The dimer model is a model of perfect matching whose popularity stems from the fact that it is exactly solvable. It is believed that the large-scale fluctuations of the height function of the dimer model is universal in a certain sense and should not depend on the microscopic properties of the graph. It turns out that in this level of generality, the well-established methods using Kasteleyn matrices become intractable.

 

 We propose a new method for examining the fluctuation of the height function which enables us to obtain a universality result for general graphs with various boundary conditions and even when the underlying surface is a Riemann surface. This provides a new proof of some old results and solves several open questions. Our methods use exact solvability in a weak sense and use some new results in the continuum instead which enables us to get universal results.

 

Ongoing joint work with Nathanael Berestycki and Benoit Laslier.

Organisé par Hugo Duminil-Copin
Contact Email: cecile@ihes.fr