Scaling limit of isoradial dimer models and the case of triangular quadri-tilings
Annales de l'I.H.P. Probabilités et statistiques, Volume 43 (2007) no. 6, p. 729-750
@article{AIHPB_2007__43_6_729_0,
     author = {de Tili\`ere, B\'eatrice},
     title = {Scaling limit of isoradial dimer models and the case of triangular quadri-tilings},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Elsevier},
     volume = {43},
     number = {6},
     year = {2007},
     pages = {729-750},
     doi = {10.1016/j.anihpb.2006.10.002},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2007__43_6_729_0}
}
de Tilière, Béatrice. Scaling limit of isoradial dimer models and the case of triangular quadri-tilings. Annales de l'I.H.P. Probabilités et statistiques, Volume 43 (2007) no. 6, pp. 729-750. doi : 10.1016/j.anihpb.2006.10.002. http://www.numdam.org/item/AIHPB_2007__43_6_729_0/

[1] S. Bochner, Harmonic Analysis and the Theory of Probabilities, Univ. of California Press, 1960. | Zbl 0068.11702

[2] O. Bodini, M. Latapy, Generalized tilings with height functions, Morfismos 7 (1) (2003) 47-68.

[3] B. De Tilière, Quadri-tilings of the plane, math.PR/0403324, Probab. Theory Related Fields, in press. | Zbl 1109.05032

[4] B. de Tilière, Dimères sur les graphes isoradiaux & modèle d'interfaces aléatoires en dimension 2+2, PhD Thesis, Université Paris XI, Orsay, 2004.

[5] N. Elkies, G. Kuperberg, M. Larsen, J. Propp, Alternating-sign matrices and domino tilings, J. Algebraic Combin. 1 (2) (1992) 111-132. | MR 1226347 | Zbl 0779.05009

[6] J. Glimm, A. Jaffe, Quantum Physics. A Functional Integral Point of View, Springer-Verlag, New York, 1981. | MR 628000 | Zbl 0461.46051

[7] I.M. Guelfand, N.Y. Vilenkin, Les distributions, Tome 4 : Applications de l'analyse harmonique, Dunod, Paris, 1967. | MR 216288

[8] R. Kenyon, Local statistics of lattice dimers, Ann. Inst. H. Poincaré Probab. Statist. 33 (5) (1997) 591-618. | Numdam | MR 1473567 | Zbl 0893.60047

[9] R. Kenyon, An Introduction to the Dimer Model, ICTP Lect. Notes, vol. XVII, 2004. | MR 2198850 | Zbl 1076.82025

[10] R. Kenyon, The planar dimer model with boundary: a survey, in: CRM Monogr. Ser., vol. 13, Amer. Math. Soc., Providence, RI, 2000, pp. 307-328. | MR 1798998 | Zbl 1026.82007

[11] R. Kenyon, Conformal invariance of domino tilings, Ann. Probab. 28 (2) (2000) 759-795. | MR 1782431 | Zbl 1043.52014

[12] R. Kenyon, Dominos and the Gaussian free field, Ann. Probab. 29 (3) (2001) 1128-1137. | MR 1872739 | Zbl 1034.82021

[13] R. Kenyon, The Laplacian and Dirac operators on critical planar graphs, Invent. Math. 150 (2) (2002) 409-439. | MR 1933589 | Zbl 1038.58037

[14] R. Kenyon, Height fluctuations in the honeycomb dimer model, math-ph/0405052.

[15] R. Kenyon, A. Okounkov, S. Sheffield, Dimers and amoebas, Ann. of Math. (2) 163 (3) (2006) 1019-1056. | MR 2215138 | Zbl pre05051319

[16] C. Mercat, Discrete period matrices and related topics, math-ph/0111043.

[17] S. Sheffield, Random Surfaces, Asterisque, vol. 304, 2005. | MR 2251117 | Zbl 1104.60002

[18] S. Sheffield, Gaussian Free Field for mathematicians, math.PR/0312099. | Zbl 1132.60072

[19] W.P. Thurston, Conway's tiling groups, Amer. Math. Monthly 97 (8) (1990) 757-773. | MR 1072815 | Zbl 0714.52007