Conformal invariance of isoradial dimer models & the case of triangular quadri-tilings
de Tilière, B.
arXiv, 0512395 / Harvested from arXiv
Text on arXiv
We consider dimer models on graphs which are bipartite, periodic and satisfy a geometric condition called {\em isoradiality}, defined in \cite{Kenyon3}. We show that the scaling limit of the height function of any such dimer model is $1/\sqrt{\pi}$ times a Gaussian free field. Triangular quadri-tilings were introduced in \cite{Bea}; they are dimer models on a family of isoradial graphs arising form rhombus tilings. By means of two height functions, they can be interpreted as random interfaces in dimension 2+2. We show that the scaling limit of each of the two height functions is $1/\sqrt{\pi}$ times a Gaussian free field, and that the two Gaussian free fields are independent.
Publié le : 2005-12-16
Classification:  Mathematics - Probability,  Mathematical Physics,  82B20,  60G15 
@article{0512395,
     author = {de Tili\`ere, B.},
     title = {Conformal invariance of isoradial dimer models \& the case of triangular
  quadri-tilings},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0512395}
}

de Tilière, B. Conformal invariance of isoradial dimer models & the case of triangular
  quadri-tilings. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0512395/