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References

  • Alcalde Cuesta, Fernando; Fernández de Córdoba, María P. Nombre de branchement d'un pseudogroupe. (French) [Number of branchings of a pseudogroup] Monatsh. Math. 163 (2011), no. 4, 389--414. MR2820370
  • Aldous, David; Lyons, Russell. Processes on unimodular random networks. Electron. J. Probab. 12 (2007), no. 54, 1454--1508. MR2354165
  • Angel, O. Growth and percolation on the uniform infinite planar triangulation. Geom. Funct. Anal. 13 (2003), no. 5, 935--974. MR2024412
  • Angel, Omer; Schramm, Oded. Uniform infinite planar triangulations. Comm. Math. Phys. 241 (2003), no. 2-3, 191--213. MR2013797
  • Avez, André. Théorème de Choquet-Deny pour les groupes à croissance non exponentielle. (French) C. R. Acad. Sci. Paris Sér. A 279 (1974), 25--28. MR0353405
  • Benjamini, Itai; Curien, Nicolas. On limits of graphs sphere packed in Euclidean space and applications. European J. Combin. 32 (2011), no. 7, 975--984. MR2825530
  • Benjamini, Itai; Curien, Nicolas. Recurrence of the $\Bbb Z^ d$-valued infinite snake via unimodularity. Electron. Commun. Probab. 17 (2012), no. 1, 10 pp. MR2872570
  • Benjamini, I.; Lyons, R.; Peres, Y.; Schramm, O. Group-invariant percolation on graphs. Geom. Funct. Anal. 9 (1999), no. 1, 29--66. MR1675890
  • Benjamini, Itai; Schramm, Oded. Harmonic functions on planar and almost planar graphs and manifolds, via circle packings. Invent. Math. 126 (1996), no. 3, 565--587. MR1419007
  • Benjamini, Itai; Schramm, Oded. Recurrence of distributional limits of finite planar graphs. Electron. J. Probab. 6 (2001), no. 23, 13 pp. (electronic). MR1873300
  • Berger, Noam. Transience, recurrence and critical behavior for long-range percolation. Comm. Math. Phys. 226 (2002), no. 3, 531--558. MR1896880
  • Biskup, Marek. Graph diameter in long-range percolation. Random Structures Algorithms 39 (2011), no. 2, 210--227. MR2850269
  • L. Bowen. Random walks on coset spaces with applications to Furstenberg entropy. preprint available on arxiv.
  • 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
  • N. Curien, L. Ménard, and G. Miermont. A view from infinity of the uniform infinite planar quadrangulation. arXiv:1201.1052.
  • Derriennic, Yves. Quelques applications du théorème ergodique sous-additif. (French) Conference on Random Walks (Kleebach, 1979) (French), pp. 183--201, 4, Astérisque, 74, Soc. Math. France, Paris, 1980. MR0588163
  • Feldman, Jacob; Moore, Calvin C. Ergodic equivalence relations, cohomology, and von Neumann algebras. I. Trans. Amer. Math. Soc. 234 (1977), no. 2, 289--324. MR0578656
  • Gaboriau, D. Invariant percolation and harmonic Dirichlet functions. Geom. Funct. Anal. 15 (2005), no. 5, 1004--1051. MR2221157
  • J. T. Gill and S. Rohde. On the Riemann surface type of random planar maps. arXiv:1101.1320.
  • Guivarc'h, Y. Sur la loi des grands nombres et le rayon spectral d'une marche aléatoire. (French) Conference on Random Walks (Kleebach, 1979) (French), pp. 47--98, 3, Astérisque, 74, Soc. Math. France, Paris, 1980. MR0588157
  • O. Gurel-Gurevich and A. Nachmias. Recurrence of planar graph limits. Ann. Maths (to appear), 2012.
  • Häggström, Olle. Infinite clusters in dependent automorphism invariant percolation on trees. Ann. Probab. 25 (1997), no. 3, 1423--1436. MR1457624
  • Ka?manovich, V. A. Brownian motion on foliations: entropy, invariant measures, mixing. (Russian) Funktsional. Anal. i Prilozhen. 22 (1988), no. 4, 82--83; translation in Funct. Anal. Appl. 22 (1988), no. 4, 326--328 (1989) MR0977003
  • Ka?manovich, V. A. Boundary and entropy of random walks in random environment. Probability theory and mathematical statistics, Vol. I (Vilnius, 1989), 573--579, "Mokslas'', Vilnius, 1990. MR1153846
  • Kaimanovich, Vadim A. Hausdorff dimension of the harmonic measure on trees. Ergodic Theory Dynam. Systems 18 (1998), no. 3, 631--660. MR1631732
  • Kaimanovich, Vadim A. Random walks on Sierpi?ski graphs: hyperbolicity and stochastic homogenization. Fractals in Graz 2001, 145--183, Trends Math., Birkhäuser, Basel, 2003. MR2091703
  • Kaimanovich, V. A.; Kifer, Y.; Rubshtein, B.-Z. Boundaries and harmonic functions for random walks with random transition probabilities. J. Theoret. Probab. 17 (2004), no. 3, 605--646. MR2091553
  • Kaimanovich, Vadim A.; Sobieczky, Florian. Stochastic homogenization of horospheric tree products. Probabilistic approach to geometry, 199--229, Adv. Stud. Pure Math., 57, Math. Soc. Japan, Tokyo, 2010. MR2648261
  • Ka?manovich, V. A.; Vershik, A. M. Random walks on discrete groups: boundary and entropy. Ann. Probab. 11 (1983), no. 3, 457--490. MR0704539
  • Kaimanovich, Vadim A.; Woess, Wolfgang. Boundary and entropy of space homogeneous Markov chains. Ann. Probab. 30 (2002), no. 1, 323--363. MR1894110
  • Kesten, Harry. Subdiffusive behavior of random walk on a random cluster. Ann. Inst. H. Poincaré Probab. Statist. 22 (1986), no. 4, 425--487. MR0871905
  • M. Krikun. Local structure of random quadrangulations. arXiv:0512304.
  • Le Gall, Jean-François. Large random planar maps and their scaling limits. European Congress of Mathematics, 253--276, Eur. Math. Soc., Zürich, 2010. MR2648329
  • Lyons, Russell; Pemantle, Robin; Peres, Yuval. Ergodic theory on Galton-Watson trees: speed of random walk and dimension of harmonic measure. Ergodic Theory Dynam. Systems 15 (1995), no. 3, 593--619. MR1336708
  • R. Lyons and Y. Peres. Probability on Trees and Networks. Current version available at http://mypage.iu.edu/~rdlyons/, In preparation.
  • Ménard, Laurent. The two uniform infinite quadrangulations of the plane have the same law. Ann. Inst. Henri Poincaré Probab. Stat. 46 (2010), no. 1, 190--208. MR2641776
  • Paulin, F. Propriétés asymptotiques des relations d'équivalences mesurées discrètes. (French) [Asymptotic properties of discrete measured equivalence relations] Markov Process. Related Fields 5 (1999), no. 2, 163--200. MR1762172
  • Soardi, Paolo M.; Woess, Wolfgang. Amenability, unimodularity, and the spectral radius of random walks on infinite graphs. Math. Z. 205 (1990), no. 3, 471--486. MR1082868


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