Uniform Infinite Planar Triangulations

Communications in Mathematical Physics

Volumn 241, Issue 2-3, 2003, Pages 191-213

  Angel, Omer ^a   Schramm, Oded ^b  

^a WEIZMANN INSTITUTE OF SCIENCE   (Israel)

^b MICROSOFT   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0242339395     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-003-0932-3     Document Type: Article

References (36)

1. Ambjørn, J.: Quantization of Geometry. Lectures presented at the 1994 Les Hauches Summer School "Fluctuating Geometries in Statistical Mechanics and Field Theory". arXiv: hep-th/9411179
2. Ambjørn, J., Durhuus, B., Jonsson, T.: Quantum Gravity, a Statistical Field Theory Approach. Cambridge Monographs on Mathematical Physics, Cambridge: Cambridge University Press, 1997
3. Ambjørn, J., Watabiki, Y.: Scaling in quantum gravity. Nucl. Phys. B 445(1), 129-142 (1995)
4. Angel, O.: Growth and Percolation on the Uniform Infinite Planar Triangulation. In preparation
5. Banderier, C., Flajolet, P., Schaeffer, G., Soria, M.: Planar maps and Airy phenomena. In: Auto-mata, lang. and prog. (Geneva, 2000), Lecture Notes in Comput. Sci., 1853, Berlin: Springer, 2000, pp. 388-402
6. Banderier, C., Flajolet, P., Schaeffer, G., Soria, M.: Random maps, coalescing saddles, singularity analysis, and Airy phenomena. In: Analysis of algorithms (Krynica Morska, 2000). Random Struc. Alg. 19(3-4), 194-246 (2001)
7. Bender, E.A., Compton, K.J., Richmond, B.L.: 0-1 laws for maps. Random Struc. Alg. 14(3), 215-237 (1999)
8. Bender, E.A., Richmond, B.L., Wormald, N.C.: Largest 4-connected components of 3-connected planar triangulations. Random Struc. Alg. 7(4), 273-285 (1995)
9. Benjamini, I., Schramm, O.: Recurrence of Distributional Limits of Finite Planar Graphs. Elec. J. Prob. 6, 23 (2001)
10. Boulatov, D.V., Kazakov, V.A.: The Ising Model on a Random Planar Lattice: the Structure of the Phase Transition and the Exact Critical Exponents. Phys. Lett. B 186(3-4), 379-384 (1987)
11. Bowick, M.J., Catterall, S.M., Thorleifsson, G.: Minimal Dynamical Triangulations of Random Surfaces. Phys. Lett. B 391(3-4), 305-309 (1997)
12. Brown, W.G.: Enumeration of triangulations of the disk. Proc. London Math. Soc. (3) 14, 746-768 (1964)
13. Chassaing, P., Schaeffer, G.: Random Planar Lattices and Integrated Super-Brownian Excursion. arXiv:math.CO/0205226
14. David, F.: Simplicial Quantum Gravity and Random Lattices. In: Gravitation et quantifications (Les Hauches, 1992), Amsterdam: North-Holland, Amsterdam, 1995, pp. 679-749, arXiv:hep-th/9303127
15. Di Francesco, P., Ginsparg, P., Zinn-Justin, J.: 2D Gravity and Random Matrices. Phys. Rep. 254(1-2), (1995)
16. Duplantier, B.: Random walks, polymers, percolation, and quantum gravity in two dimensions. In: STATPHYS 20 (Paris, 1998). Phys. A 263(1-4), 452-465 (1999)
17. Duplantier, B.: Random walks and quantum gravity in two dimensions. Phys. Rev. Lett. 81(25), 5489-5492 (1998)
18. Gao, Z., Richmond, B.L.: Root vertex valency distributions of rooted maps and rooted triangulations. Europ. J. Comb. 15(5), 483-490 (1994)
19. Gao, Z., Wormald, N.C.: The size of the largest component in random planar maps. Siam J. Disc. Math. 12(2), 217-228 (1999)
20. Goulden, I.P., Jackson, D.M.: Combinatorial enumeration. New York: Wiley, 1983
21. He, Z.X., Schramm, O.: Hyperbolic and parabolic packings. Disc. Comp. Geom. 14(2), 123-149 (1995)
22. Knizhnik, V.G., Polyakov, A.M., Zamolodchikov, A.B.: Fractal structure of 2D-quantum gravity. Mod. Phys. Lett. A 3(8), 819-826 (1988)
23. Koebe, P.: Kontaktprobleme der konformen abbildung, Berichte Verhande. Sächs. Akad. Wiss. Leipzig, Math. -Phys. Klasse 88, 141-164 (1936)
24. Lawler, G., Schramm, O., Werner, W.: Values of Brownian intersection exponents. I. Half-plane exponents. Acta Math. 187(2), 237-273 (2001)
25. Lawler, G., Schramm, O., Werner, W.: Values of Brownian intersection exponents. II. Plane exponents. Acta Math. 187(2), 275-308 (2001)
26. Lawler, G., Schramm, O., Werner, W.: Values of Brownian intersection exponents III: Two-sided exponents. Ann. Inst. H. Poincare Prob. Stat. 38(1), 109-123 (2002)
27. Lyons, R., Peres, Y.: Probability on Trees and Networks, www.math.gatech.edu/rdlyons/prbtree/prbtree.html
28. Richmond, B.L., Wormald, N.C.: Random triangulations of the plane. Euro. J. Comb. 9(1), 61-71 (1988)
29. Richmond, B.L., Wormald, N.C.: Almost all maps are asymmetric. J. Comb. Theory Ser. B 63(1), 1-7 (1995)
30. Schaeffer, G.: Conjugaison s'arbres et cartes combinatoires aléatoires. PhD. Thesis, Université Bordeaux I, 1998, Bordeaux
31. Smirnov, S.: Critical percolation in the plane: conformal invariance, Cardy's formula, scaling limits. C. R. Acad. Sci. Paris Sć4. I Math. 333(3), 239-244 (2001)
32. Tutte, W.T.: A census of planar triangulations. Canad. J. Math. 14, 21-38 (1962)
33. Tutte, W.T.: A census of Hamiltonian polygons. Canad. J. Math. 14, 402-417 (1962)
34. Tutte, W.T.: A census of slicings. Canad. J. Math. 14, 708-722 (1962)
35. Tutte, W.T.:Acensusof planar maps. Canad. J. Math. 15, 249-271 (1963)
36. Tutte, W.T.: On the enumeration of convex polyhedra. J. Comb. The. Ser. B 28(2), 105-126 (1980)