References

• Aldous, David; Pitman, Jim. Tree-valued Markov chains derived from Galton-Watson processes. Ann. Inst. H. Poincaré Probab. Statist. 34 (1998), no. 5, 637--686. MR1641670
• S. Alexander and R. Orbach, Density of states on fractals: ''fractons'', J. Physique (Paris) Lett. 43 (1982), 625-631.
• Angel, Omer; Schramm, Oded. Uniform infinite planar triangulations. Comm. Math. Phys. 241 (2003), no. 2-3, 191--213. MR2013797
• Barlow, Martin T.; Kumagai, Takashi. Random walk on the incipient infinite cluster on trees. Illinois J. Math. 50 (2006), no. 1-4, ISBN: 0-9746986-1-X 33--65 (electronic). MR2247823
• Berger, Noam. Transience, recurrence and critical behavior for long-range percolation. Comm. Math. Phys. 226 (2002), no. 3, 531--558. MR1896880
• Benjamini, Itai; Schramm, Oded. Recurrence of distributional limits of finite planar graphs. Electron. J. Probab. 6 (2001), no. 23, 13 pp. (electronic). MR1873300
• J. Bettinelli, Scaling limit of random planar quadrangulations with a boundary. Ann. Inst. H. Poincaré Probab. Statist. (to appear)
• Bouttier, J.; Di Francesco, P.; Guitter, E. Planar maps as labeled mobiles. Electron. J. Combin. 11 (2004), no. 1, Research Paper 69, 27 pp. MR2097335
• Chassaing, Philippe; Durhuus, Bergfinnur. Local limit of labeled trees and expected volume growth in a random quadrangulation. Ann. Probab. 34 (2006), no. 3, 879--917. MR2243873
• Curien, N.; Ménard, L.; Miermont, G. A view from infinity of the uniform infinite planar quadrangulation. ALEA Lat. Am. J. Probab. Math. Stat. 10 (2013), no. 1, 45--88. MR3083919
• Durhuus, Bergfinnur; Jonsson, Thordur; Wheater, John F. The spectral dimension of generic trees. J. Stat. Phys. 128 (2007), no. 5, 1237--1260. MR2348795
• Fujii, Ichiro; Kumagai, Takashi. Heat kernel estimates on the incipient infinite cluster for critical branching processes. Proceedings of RIMS Workshop on Stochastic Analysis and Applications, 85--95, RIMS Kôkyûroku Bessatsu, B6, Res. Inst. Math. Sci. (RIMS), Kyoto, 2008. MR2407556
• Gurel-Gurevich, Ori; Nachmias, Asaf. Recurrence of planar graph limits. Ann. of Math. (2) 177 (2013), no. 2, 761--781. MR3010812
• Gut, Allan. Stopped random walks. Limit theorems and applications. Second edition. Springer Series in Operations Research and Financial Engineering. Springer, New York, 2009. xiv+263 pp. ISBN: 978-0-387-87834-8 MR2489436
• Janson, Svante; Jonsson, Thordur; Stefánsson, Sigurdur Örn. Random trees with superexponential branching weights. J. Phys. A 44 (2011), no. 48, 485002, 16 pp. MR2860856
• Janson, Svante. Simply generated trees, conditioned Galton-Watson trees, random allocations and condensation. Probab. Surv. 9 (2012), 103--252. MR2908619
• S. Janson and S. Ö. Stefánsson, Scaling limits of random planar maps with a unique large face. (To appear.) arXiv:1212.5072.
• Jonsson, Thordur; Stefánsson, Sigurdur Örn. Condensation in nongeneric trees. J. Stat. Phys. 142 (2011), no. 2, 277--313. MR2764126
• Kennedy, Douglas P. The Galton-Watson process conditioned on the total progeny. J. Appl. Probability 12 (1975), no. 4, 800--806. MR0386042
• Kesten, Harry. Subdiffusive behavior of random walk on a random cluster. Ann. Inst. H. Poincaré Probab. Statist. 22 (1986), no. 4, 425--487. MR0871905
• Komlós, J.; Major, P.; Tusnády, G. An approximation of partial sums of independent ${\rm RV}$'s and the sample ${\rm DF}$. I. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 32 (1975), 111--131. MR0375412
• Kozma, Gady; Nachmias, Asaf. The Alexander-Orbach conjecture holds in high dimensions. Invent. Math. 178 (2009), no. 3, 635--654. MR2551766
• M. Krikun, Local structure of random quadrangulations. arXiv:0512304.
• Kumagai, Takashi; Misumi, Jun. Heat kernel estimates for strongly recurrent random walk on random media. J. Theoret. Probab. 21 (2008), no. 4, 910--935. MR2443641
• Le Gall, Jean-Francois; Miermont, Grégory. Scaling limits of random trees and planar maps. Probability and statistical physics in two and more dimensions, 155--211, Clay Math. Proc., 15, Amer. Math. Soc., Providence, RI, 2012. MR3025391
• Le Gall, Jean-Francois. The topological structure of scaling limits of large planar maps. Invent. Math. 169 (2007), no. 3, 621--670. MR2336042
• Le Gall, Jean-Francois; Miermont, Grégory. Scaling limits of random planar maps with large faces. Ann. Probab. 39 (2011), no. 1, 1--69. MR2778796
• Le Gall, Jean-Francois. Uniqueness and universality of the Brownian map. Ann. Probab. 41 (2013), no. 4, 2880--2960. MR3112934
• R. Lyons and Y. Peres, Probability on trees and networks. CUP, 2005.
• Marckert, Jean-Francois; Miermont, Grégory. Invariance principles for random bipartite planar maps. Ann. Probab. 35 (2007), no. 5, 1642--1705. MR2349571
• L. Ménard and P. Nolin, Percolation on uniform infinite planar maps, arXiv:1302.2851.
• Miermont, Grégory. The Brownian map is the scaling limit of uniform random plane quadrangulations. Acta Math. 210 (2013), no. 2, 319--401. MR3070569
• Miermont, Grégory. An invariance principle for random planar maps. Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, 39--57, Discrete Math. Theor. Comput. Sci. Proc., AG, Assoc. Discrete Math. Theor. Comput. Sci., Nancy, 2006. MR2509622
• G. Schaeffer, Conjugaison d’arbres et cartes combinatoires aléatoires. Ph.D. thesis, Univ. Bordeaux I (1998).