References

• Louigi Addario-Berry and Nicholas Leavitt. Random infinite squarings of rectangles. arXiv:1405.2870 [math.PR], 2014.
• Aldous, David; Steele, J. Michael. The objective method: probabilistic combinatorial optimization and local weak convergence. Probability on discrete structures, 1--72, Encyclopaedia Math. Sci., 110, Springer, Berlin, 2004. MR2023650 http://www.stat.berkeley.edu/~aldous/Papers/me101.pdf
• Angel, Omer; Schramm, Oded. Uniform infinite planar triangulations. Comm. Math. Phys. 241 (2003), no. 2-3, 191--213. MR2013797 http://dx.doi.org/10.1007/978-1-4419-9675-6_16
• Bender, Edward A.; Canfield, E. Rodney. Face sizes of $3$-polytopes. J. Combin. Theory Ser. B 46 (1989), no. 1, 58--65. MR0982855 http://dx.doi.org/10.1016/0095-8956(89)90007-5
• Benjamini, Itai; Schramm, Oded. Recurrence of distributional limits of finite planar graphs. Electron. J. Probab. 6 (2001), no. 23, 13 pp. (electronic). MR1873300 http://arxiv.org/abs/math/0011019
• Bettinelli, Jérémie. Increasing forests and quadrangulations via a bijective approach. J. Combin. Theory Ser. A 122 (2014), 107--125. MR3127680 http://arxiv.org/abs/1203.2365
• Brooks, R. L.; Smith, C. A. B.; Stone, A. H.; Tutte, W. T. The dissection of rectangles into squares. Duke Math. J. 7, (1940). 312--340. MR0003040
• 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 http://dx.doi.org/10.1214/009117905000000774
• Evans, Steven N.; Grübel, Rudolf; Wakolbinger, Anton. Trickle-down processes and their boundaries. Electron. J. Probab. 17 (2012), no. 1, 58 pp. MR2869248 http://arxiv.org/abs/1010.0453
• Fusy, Éric; Schaeffer, Gilles; Poulalhon, Dominique. Dissections, orientations, and trees with applications to optimal mesh encoding and random sampling. ACM Trans. Algorithms 4 (2008), no. 2, Art. 19, 48 pp. MR2419116 http://arxiv.org/abs/0810.2608
• Gurel-Gurevich, Ori; Nachmias, Asaf. Recurrence of planar graph limits. Ann. of Math. (2) 177 (2013), no. 2, 761--781. MR3010812 http://arxiv.org/abs/1206.0707
• Lando, Sergei K.; Zvonkin, Alexander K. Graphs on surfaces and their applications. With an appendix by Don B. Zagier. Encyclopaedia of Mathematical Sciences, 141. Low-Dimensional Topology, II. Springer-Verlag, Berlin, 2004. xvi+455 pp. ISBN: 3-540-00203-0 MR2036721
• Le Gall, Jean-François; 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 http://www.math.u-psud.fr/~jflegall/Cours-Buziosf.pdf
• Luczak, Malwina; Winkler, Peter. Building uniformly random subtrees. Random Structures Algorithms 24 (2004), no. 4, 420--443. MR2060629 http://www.math.dartmouth.edu/~pw/papers/birds.ps
• Marckert, Jean-François. The rotation correspondence is asymptotically a dilatation. Random Structures Algorithms 24 (2004), no. 2, 118--132. MR2035871 http://www.labri.fr/perso/marckert/propre.pdf
• Mullin, R. C.; Schellenberg, P. J. The enumeration of $c$-nets via quadrangulations. J. Combinatorial Theory 4 1968 259--276. MR0218275 http://www.sciencedirect.com/science/article/pii/S0021980068800079#