Grands graphes planaires aléatoires et carte brownienne [d'après Jean-François Le Gall]
Séminaire Bourbaki Volume 2007/2008 Exposés 982-996, Astérisque, no. 326 (2009), Talk no. 992, 22 p.
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Beffara, Vincent. Grands graphes planaires aléatoires et carte brownienne [d'après Jean-François Le Gall], in Séminaire Bourbaki Volume 2007/2008 Exposés 982-996, Astérisque, no. 326 (2009), Talk no. 992, 22 p. http://archive.numdam.org/item/AST_2009__326__299_0/

[1] D. Aldous - The continuum random tree I, Ann. Probab. 19 (1991), p. 1-28. | DOI | MR | Zbl

[2] O. Angel - Growth and percolation on the uniform infinite planar triangulation, Geom. Fund. Anal. 13 (2003), p. 935-974. | DOI | MR | Zbl

[3] O. Angel & O. Schramm - Uniform infinite planar triangulations, Comm. Math. Phys. 241 (2003), p. 191-213. | DOI | MR | Zbl

[4] F. Bonahon - Geodesic laminations on surfaces, in Laminations and foliations in dynamics, geometry and topology (Stony Brook, NY, 1998), Contemp. Math., vol. 269, Amer. Math. Soc., 2001, p. 1-37. | DOI | MR | Zbl

[5] J. Bouttier - Physique statistique des surfaces aléatoires et combinatoire bijective des cartes planaires, Thèse, Université Paris 6, 2005.

[6] J. Bouttier, P. Di Francesco & E. Guitter - Planar maps as labeled mobiles, Electron. J. Combin. 11 (2004), Research Paper 69. | EuDML | MR | Zbl

[7] J. Bouttier & E. Guitter - Statistics of geodesies in large quadrangulations, J. Phys. A : Math. Theor. 41 (2008), 145001. | DOI | MR | Zbl

[8] D. Burago, Y. Burago & S. Ivanov - A course in metric geometry, Graduate Studies in Math., vol. 33, Amer. Math. Soc., 2001. | DOI | MR | Zbl

[9] P. Chassaing & G. Schaeffer - Random planar lattices and integrated superBrownian excursion, Probab. Theory Related Fields 128 (2004), p. 161-212. | DOI | MR | Zbl

[10] R. Cori & B. Vauquelin - Planar maps are well labeled trees, Canad. J. Math. 33 (1981), p. 1023-1042. | DOI | MR | Zbl

[11] B. Duplantier& S. Sheffield - Liouville quantum gravity and KPZ, prépublication arXiv:0808.1560, 2008. | MR | Zbl

[12] B. Duplantier & S. Sheffield -, Duality and KPZ in Liouville quantum gravity, prépublication arXiv:0901.0277, 2009. | MR

[13] T. Duquesne & J.-F. Le Gall - Probabilistic and fractal aspects of Lévy trees, Probab. Theory Related Fields 131 (2005), p. 553-603. | DOI | MR | Zbl

[14] M. Gromov - Metric structures for Riemannian and non-Riemannian spaces, Progress in Math., vol. 152, Birkhäuser, 1999. | MR | Zbl

[15] V. G. Knizhnik, A. M. Polyakov & A. B. Zamolodchikov - Fractal structure of 2D-quantum gravity, Modern Phys. Lett. A 3 (1988), p. 819-826. | DOI | MR

[16] S. K. Lando & A. K. Zvonkin - Graphs on surfaces and their applications, Encyclopaedia of Math. Sciences, vol. 141, Springer, 2004. | DOI | MR | Zbl

[17] J.-F. Le Gall - A conditional limit theorem for tree-indexed random walk, Stochastic Process. Appl. 116 (2006), p. 539-567. | DOI | MR | Zbl

[18] J.-F. Le Gall -, Random real trees, Ann. Fac. Sci. Toulouse Math. 15 (2006), p. 35-62. | DOI | EuDML | Numdam | MR | Zbl

[19] J.-F. Le Gall -, The topological structure of scaling limits of large planar maps, Invent. Math. 169 (2007), p. 621-670. | DOI | MR | Zbl

[20] J.-F. Le Gall -, Geodesics in large planar maps and in the Brownian map, prépublication arXiv:0804.3012. | MR | Zbl

[21] J.-F. Le Gall & F. Paulin - Scaling limits of bipartite planar maps are homeomorphic to the 2-sphere, Geom. Funct. Anal. 18 (2008), p. 893-918. | DOI | MR | Zbl

[22] J.-F. Le Gall & M. Weill - Conditioned Brownian trees, Ann. Inst. H. Poincaré Probab. Statist. 42 (2006), p. 455-489. | DOI | EuDML | Numdam | MR | Zbl

[23] J.-F. Marckert & G. Miermont - Invariance principles for random bipartite planar maps, Ann. Probab. 35 (2007), p. 1642-1705. | DOI | MR | Zbl

[24] J.-F. Marckert & A. Mokkadem - Limit of normalized quadrangulations : the Brownian map, Ann. Probab. 34 (2006), p. 2144-2202. | DOI | MR | Zbl

[25] E. Maurel-Segala - Étude de l'énergie libre de certains modèles matriciels, grandes déviations et relation avec des objets combinatoires, Thèse, ENS de Lyon, 2007.

[26] G. Miermont - On the sphericity of scaling limits of random planar quadrangulations, Electron. Commun. Probab. 13 (2008), p. 248-257. | DOI | EuDML | MR | Zbl

[27] G. Miermont & M. Weill - Radius and profile of random planar maps with faces of arbitrary degrees, Electron. J. Probab. 13 (2008), p. 79-106. | DOI | EuDML | MR | Zbl

[28] R. L. Moore - Concerning upper semi-continuous collections of continua, Trans. Amer. Math. Soc. 27 (1925), p. 416-428. | DOI | JFM | MR

[29] G. Schaeffer - Conjugaison d'arbres et cartes combinatoires aléatoires, Thèse, Université de Bordeaux I, 1998.

[30] S. Sheffield - Gaussian free fields for mathematicians, Probab. Theory Related Fields 139 (2007), p. 521-541. | DOI | MR | Zbl

[31] W. Vervaat - A relation between Brownian bridge and Brownian excursion, Ann. Probab. 7 (1979), p. 143-149. | DOI | MR | Zbl

[32] M. Weill - Asymptotics for rooted bipartite planar maps and scaling limits of two-type spatial trees, Electron. J. Probab. 12 (2007), p. 887-925. | DOI | EuDML | MR | Zbl