Scaling limit of isoradial dimer models and the case of triangular quadri-tilings

 Access to full text

 Full (PDF)

1. [1] S. Bochner, Harmonic Analysis and the Theory of Probabilities, Univ. of California Press, 1960. Zbl0068.11702
2. [2] O. Bodini, M. Latapy, Generalized tilings with height functions, Morfismos7 (1) (2003) 47-68. 
3. [3] B. de Tilière, Quadri-tilings of the plane, math.PR/0403324, Probab. Theory Related Fields, in press. Zbl1109.05032
4. [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. [5] N. Elkies, G. Kuperberg, M. Larsen, J. Propp, Alternating-sign matrices and domino tilings, J. Algebraic Combin.1 (2) (1992) 111-132. Zbl0779.05009MR1226347
6. [6] J. Glimm, A. Jaffe, Quantum Physics. A Functional Integral Point of View, Springer-Verlag, New York, 1981. Zbl0461.46051MR628000
7. [7] I.M. Guelfand, N.Y. Vilenkin, Les distributions, Tome 4 : Applications de l'analyse harmonique, Dunod, Paris, 1967. Zbl0219.46032MR216288
8. [8] R. Kenyon, Local statistics of lattice dimers, Ann. Inst. H. Poincaré Probab. Statist.33 (5) (1997) 591-618. Zbl0893.60047MR1473567
9. [9] R. Kenyon, An Introduction to the Dimer Model, ICTP Lect. Notes, vol. XVII, 2004. Zbl1076.82025MR2198850
10. [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. Zbl1026.82007MR1798998
11. [11] R. Kenyon, Conformal invariance of domino tilings, Ann. Probab.28 (2) (2000) 759-795. Zbl1043.52014MR1782431
12. [12] R. Kenyon, Dominos and the Gaussian free field, Ann. Probab.29 (3) (2001) 1128-1137. Zbl1034.82021MR1872739
13. [13] R. Kenyon, The Laplacian and Dirac operators on critical planar graphs, Invent. Math.150 (2) (2002) 409-439. Zbl1038.58037MR1933589
14. [14] R. Kenyon, Height fluctuations in the honeycomb dimer model, math-ph/0405052. Zbl1157.82028
15. [15] R. Kenyon, A. Okounkov, S. Sheffield, Dimers and amoebas, Ann. of Math. (2)163 (3) (2006) 1019-1056. Zbl1154.82007MR2215138
16. [16] C. Mercat, Discrete period matrices and related topics, math-ph/0111043. 
17. [17] S. Sheffield, Random Surfaces, Asterisque, vol. 304, 2005. Zbl1104.60002MR2251117
18. [18] S. Sheffield, Gaussian Free Field for mathematicians, math.PR/0312099. Zbl1132.60072
19. [19] W.P. Thurston, Conway's tiling groups, Amer. Math. Monthly97 (8) (1990) 757-773. Zbl0714.52007MR1072815