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Volumn 18, Issue 3, 2008, Pages 893-918

Scaling limits of bipartite planar maps are homeomorphic to the 2-sphere

Author keywords

Brownian snake; Geodesic lamination; Random planar map; Random tree; Scaling limit

Indexed keywords


EID: 52449120370     PISSN: 1016443X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00039-008-0671-x     Document Type: Article
Times cited : (105)

References (33)
  • 1
    • 3042515241 scopus 로고    scopus 로고
    • Avoiding probabilities for Brownian snakes and super-Brownian motion
    • 27pp
    • [AW] R. ABRAHAM, W. WERNER, Avoiding probabilities for Brownian snakes and super-Brownian motion, Electron. J. Probab. 2:3 (1997), 27pp.
    • (1997) Electron. J. Probab , vol.2 , Issue.3
    • ABRAHAM, R.1    WERNER, W.2
  • 2
    • 0003296611 scopus 로고
    • The continuum random tree I
    • Al1
    • [Al1] D. ALDOUS, The continuum random tree I, Ann. Probab. 19 (1991), 1-28.
    • (1991) Ann. Probab , vol.19 , pp. 1-28
    • ALDOUS, D.1
  • 3
    • 0003296611 scopus 로고
    • The continuum random tree III
    • Al2
    • [Al2] D. ALDOUS, The continuum random tree III, Ann. Probab. 21 (1993), 248-289.
    • (1993) Ann. Probab , vol.21 , pp. 248-289
    • ALDOUS, D.1
  • 4
    • 21344497620 scopus 로고
    • Triangulating the circle at random
    • Al3
    • [Al3] D. ALDOUS, Triangulating the circle at random, Amer. Math. Monthly 101 (1994), 223-233.
    • (1994) Amer. Math. Monthly , vol.101 , pp. 223-233
    • ALDOUS, D.1
  • 5
    • 0040847184 scopus 로고
    • Recursive self-similarity for random trees, random triangulations and Brownian excursion
    • Al4
    • [Al4] D. ALDOUS, Recursive self-similarity for random trees, random triangulations and Brownian excursion, Ann. Probab. 22 (1994), 527-545.
    • (1994) Ann. Probab , vol.22 , pp. 527-545
    • ALDOUS, D.1
  • 6
    • 0001238356 scopus 로고    scopus 로고
    • J. BIRMAN, C. SERIES, Geodesics with bounded intersection number on surfaces are sparsely distributed, Topology 24 (1985), 217-225.
    • [BS] J. BIRMAN, C. SERIES, Geodesics with bounded intersection number on surfaces are sparsely distributed, Topology 24 (1985), 217-225.
  • 7
    • 85083866416 scopus 로고    scopus 로고
    • F. BONAHON, Geodesic laminations on surfaces, in Laminations and Foliations in Dynamics, Geometry and Topology (Stony Brook, NY, 1998), Contemp. Math. 269, Amer. Math. Soc. (2001), 1-37.
    • [Bo] F. BONAHON, Geodesic laminations on surfaces, in "Laminations and Foliations in Dynamics, Geometry and Topology (Stony Brook, NY, 1998), Contemp. Math. 269, Amer. Math. Soc. (2001), 1-37.
  • 9
    • 85083866118 scopus 로고    scopus 로고
    • J. BOUTTIER, Physique statistique des surfaces aléatoires et combinatoire bijective des cartes planaires, PhD thesis, Université Paris 6, 2005; see also http://tel.ccsd.cnrs.fr/documents/ archives0/00/01/06/51/index.html
    • [Bout] J. BOUTTIER, Physique statistique des surfaces aléatoires et combinatoire bijective des cartes planaires, PhD thesis, Université Paris 6, 2005; see also http://tel.ccsd.cnrs.fr/documents/ archives0/00/01/06/51/index.html
  • 14
    • 0842346773 scopus 로고    scopus 로고
    • Random planar lattices and integrated super-Brownian excursion
    • [CS] P. CHASSAING, G. SCHAEFFER, Random planar lattices and integrated super-Brownian excursion, Probab. Th. Rel. Fields 128 (2004), 161-212.
    • (2004) Probab. Th. Rel. Fields , vol.128 , pp. 161-212
    • CHASSAING, P.1    SCHAEFFER, G.2
  • 15
    • 15544389808 scopus 로고    scopus 로고
    • Probabilistic and fractal aspects of Lévy trees
    • [DL] T. DUQUESNE, J.F. LE GALL, Probabilistic and fractal aspects of Lévy trees, Probab. Th. Rel. Fields 131 (2005), 553-603.
    • (2005) Probab. Th. Rel. Fields , vol.131 , pp. 553-603
    • DUQUESNE, T.1    LE GALL, J.F.2
  • 17
    • 84972526610 scopus 로고
    • Dendrology of groups in low ℚ-ranks
    • [GS] H. GILLET, P. SHALEN, Dendrology of groups in low ℚ-ranks, J. Diff. Geom. 32 (1990), 605-712.
    • (1990) J. Diff. Geom , vol.32 , pp. 605-712
    • GILLET, H.1    SHALEN, P.2
  • 20
    • 34548064980 scopus 로고    scopus 로고
    • The topological structure of scaling limits of large planar maps
    • L2
    • [L2] J.F. LE GALL, The topological structure of scaling limits of large planar maps, Invent. Math. 169 (2007), 621-670.
    • (2007) Invent. Math , vol.169 , pp. 621-670
    • LE GALL, J.F.1
  • 21
    • 33745728251 scopus 로고    scopus 로고
    • J.F. LE GALL, M. WEILL, Conditioned Brownian trees, Ann. Inst. H. Poincaré, Probab. Stat. 42 (2006), 455-489.
    • [LW] J.F. LE GALL, M. WEILL, Conditioned Brownian trees, Ann. Inst. H. Poincaré, Probab. Stat. 42 (2006), 455-489.
  • 22
    • 0040238243 scopus 로고    scopus 로고
    • Geometric group actions on trees
    • [LeP] G. LEVITT, F. PAULIN, Geometric group actions on trees, Amer. Math. J. 119 (1997), 83-102.
    • (1997) Amer. Math. J , vol.119 , pp. 83-102
    • LEVITT, G.1    PAULIN, F.2
  • 23
    • 38749135683 scopus 로고    scopus 로고
    • Invariance principles for random bipartite planar maps
    • [MM] J.F. MARCKERT, G. MIERMONT, Invariance principles for random bipartite planar maps, Ann. Probab. 35 (2007), 1642-1705.
    • (2007) Ann. Probab , vol.35 , pp. 1642-1705
    • MARCKERT, J.F.1    MIERMONT, G.2
  • 24
    • 33947505882 scopus 로고    scopus 로고
    • Limits of normalized quadrangulations. The Brownian map
    • [MMo] J.F. MARCKERT, A. MOKKADEM, Limits of normalized quadrangulations. The Brownian map, Ann. Probab. 34 (2006), 2144-2202.
    • (2006) Ann. Probab , vol.34 , pp. 2144-2202
    • MARCKERT, J.F.1    MOKKADEM, A.2
  • 26
    • 85083867556 scopus 로고    scopus 로고
    • G. MIERMONT, An invariance principle for random planar maps, in Proceedings Fourth Colloquium on Mathematics and Computer Science CMCS'06 (Nancy, France), (2006), 39-58 (electronic).
    • [Mi] G. MIERMONT, An invariance principle for random planar maps, in "Proceedings Fourth Colloquium on Mathematics and Computer Science CMCS'06 (Nancy, France), (2006), 39-58 (electronic).
  • 27
    • 0000427353 scopus 로고
    • Concerning upper-semicontinuous collections of continua
    • [Mo] R.L. MOORE, Concerning upper-semicontinuous collections of continua, Trans. Amer. Math. Soc. 25 (1925), 416-428.
    • (1925) Trans. Amer. Math. Soc , vol.25 , pp. 416-428
    • MOORE, R.L.1
  • 28
    • 51249168650 scopus 로고
    • J.-P. OTAL, Relative growth rate of closed geodesics on a surface under varying hyperbolic structures
    • [MorO] J. MORGAN, J.-P. OTAL, Relative growth rate of closed geodesics on a surface under varying hyperbolic structures, Comm. Math. Helv. 68 (1993), 171-208.
    • (1993) Comm. Math. Helv , vol.68 , pp. 171-208
    • MORGAN, J.1
  • 29
    • 0000181446 scopus 로고
    • Valuations, trees and degeneration of hyperbolic structures I
    • [MorS] J. MORGAN, P. SHALEN, Valuations, trees and degeneration of hyperbolic structures I, Ann. Math. 122 (1985), 398-476.
    • (1985) Ann. Math , vol.122 , pp. 398-476
    • MORGAN, J.1    SHALEN, P.2
  • 30
    • 0002832883 scopus 로고
    • Topologie de Gromov équivariante, structures hyperboliques et arbres réels
    • [P] F. PAULIN, Topologie de Gromov équivariante, structures hyperboliques et arbres réels, Invent. Math. 94 (1988), 53-80.
    • (1988) Invent. Math , vol.94 , pp. 53-80
    • PAULIN, F.1
  • 31
    • 85083867281 scopus 로고    scopus 로고
    • G. SCHAEFFER, Conjugaison d'arbres et cartes combinatoires aléatoires, PhD thesis, Université Bordeaux I (1998); see also http://www.lix.polytechnique.fr/~schaeffe/Biblio/
    • [S] G. SCHAEFFER, Conjugaison d'arbres et cartes combinatoires aléatoires, PhD thesis, Université Bordeaux I (1998); see also http://www.lix.polytechnique.fr/~schaeffe/Biblio/
  • 32
    • 84966239529 scopus 로고
    • Three dimensional manifolds, Kleinian groups and hyperbolic geometry
    • [T] W. THURSTON, Three dimensional manifolds, Kleinian groups and hyperbolic geometry, Bull. Amer. Math. Soc. 6 (1982), 357-381.
    • (1982) Bull. Amer. Math. Soc , vol.6 , pp. 357-381
    • THURSTON, W.1
  • 33
    • 34948886666 scopus 로고    scopus 로고
    • Asymptotics for rooted bipartite planar maps and scaling limits of two-type spatial trees
    • [W] M. WEILL, Asymptotics for rooted bipartite planar maps and scaling limits of two-type spatial trees, Electron. J. Probab. 12 (2007), 862-925.
    • (2007) Electron. J. Probab , vol.12 , pp. 862-925
    • WEILL, M.1


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