DE TILIERE, Béatrice - Topologie et Dynamique, Université Paris-Sud, Bât. 425, 91405 Orsay cedex

Abstract :

Quadri-tilings of the plane are tilings by quadrilaterals made of adjacent right triangles. Quadri-tilings are in bijection with dimer configurations on graphs arising from rhombus tilings of the plane. Assigning ``critical'' weights to the edges of such a graph, we construct a natural explicit Gibbs measure, and prove that it is asymptotically independent of the structure of the graph. We give an explicit expression for a measure on the set of dimer configurations of all graphs arising from 60-degree rhombus tilings of the plane, whose marginals are the above Gibbs measures. We construct two ``height functions'' on 60 degrees-rhombus quadri-tilings, and thereby interpret them as surfaces in a 4-dimensional space.

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Contact : Beatrice.detiliere@math.u-psud.fr