D. Aldous, The Continuum Random Tree. I, The Annals of Probability, vol.19, issue.1, pp.1-28, 1991.
DOI : 10.1214/aop/1176990534

D. Aldous, Tree-based models for random distribution of mass, Journal of Statistical Physics, vol.18, issue.381, pp.625-641, 1993.
DOI : 10.1007/BF01054343

K. Appel and W. Haken, Every planar map is four colorable, Bulletin of the American Mathematical Society, vol.82, issue.5, pp.711-712, 1976.
DOI : 10.1090/S0002-9904-1976-14122-5

URL : http://projecteuclid.org/download/pdf_1/euclid.bams/1183538218

R. Bacher and A. Vdovina, Counting 1-vertex triangulations of oriented surfaces, Discrete Mathematics, vol.246, issue.1-3, pp.13-27, 1999.
DOI : 10.1016/S0012-365X(01)00249-7

C. Banderier and P. Flajolet, Basic analytic combinatorics of directed lattice paths, Theoretical Computer Science, vol.281, issue.1-2, pp.37-80, 2002.
DOI : 10.1016/S0304-3975(02)00007-5

E. Bender, Z. C. Gao, and L. B. Richmond, The map asymptotics constant t g . Electron, J. Combin, vol.15, 2008.

E. A. Bender, E. R. Canfield, and R. W. Robinson, The asymptotic number of tree-rooted maps on a surface, Journal of Combinatorial Theory, Series A, vol.48, issue.2, pp.156-164, 1988.
DOI : 10.1016/0097-3165(88)90002-7

E. Bender, Some unsolved problems in map enumeration, Bull. Inst. Combin . Appl, vol.3, pp.51-56, 1991.

A. Edward, E. R. Bender, and . Canfield, The asymptotic number of rooted maps on a surface, J. Combin. Theory Ser. A, vol.43, issue.2, pp.244-257, 1986.

A. Edward, E. R. Bender, and . Canfield, The number of rooted maps on an orientable surface, J. Combin. Theory Ser. B, vol.53, issue.2, pp.293-299, 1991.

A. Edward, E. R. Bender, and . Canfield, The number of degree-restricted rooted maps on the sphere, SIAM J. Discrete Math, vol.7, issue.1, pp.9-15, 1994.

E. A. Bender, E. R. Canfield, and L. Bruce-richmond, The asymptotic number of rooted maps on a surface., Journal of Combinatorial Theory, Series A, vol.63, issue.2, pp.318-329, 1993.
DOI : 10.1016/0097-3165(93)90063-E

E. A. Bender, Z. Gao, L. Bruce-richmond, and N. C. Wormald, Asymptotic properties of rooted 3-connected maps on surfaces, Journal of the Australian Mathematical Society, vol.31, issue.01, pp.31-41, 1996.
DOI : 10.1016/0097-3165(93)90097-R

E. A. Bender, Z. Gao, C. Nicholas, and . Wormald, The number of labeled 2-connected planar graphs, Electron. J. Combin.Research Paper, vol.9, issue.13, p.pp, 2002.

A. Edward, N. C. Bender, and . Wormald, The asymptotic number of rooted nonseparable maps on a surface, J. Combin. Theory Ser. A, vol.49, issue.2, pp.370-380, 1988.

O. Bernardi, Combinatoire des cartes et polynôme de Tutte, Thèse de doctorat, 2006.

O. Bernardi, Bijective counting of tree-rooted maps and shuffles of parenthesis systems, Electron. J. Combin, vol.14, issue.36, p.pp, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00018111

O. Bernardi and G. Chapuy, A bijection for covered maps on orientable surfaces, Electronic Notes in Discrete Mathematics, vol.31, p.31, 2008.
DOI : 10.1016/j.endm.2008.06.010

URL : https://hal.archives-ouvertes.fr/hal-00713488

O. Bernardi and G. Chapuy, A bijection for covered maps on orientable surfaces, or the shortest path from Harer-Zagier's to Adrianov's formulae Article soumis, 2009.

P. Billingsley, Convergence of probability measures, 1968.
DOI : 10.1002/9780470316962

P. Billingsley, Probability and measure Wiley Series in Probability and Mathematical Statistics, 1995.

M. Bousquet-mélou and S. Janson, The density of the ISE and local limit laws for embedded trees, The Annals of Applied Probability, vol.16, issue.3, pp.1597-1632, 2006.
DOI : 10.1214/105051606000000213

M. Bousquet-mélou and G. Schaeffer, Enumeration of Planar Constellations, Advances in Applied Mathematics, vol.24, issue.4, pp.337-368, 2000.
DOI : 10.1006/aama.1999.0673

J. Bouttier, P. D. Francesco, and E. Guitter, Geodesic distance in planar graphs, Nuclear Physics B, vol.663, issue.3, pp.535-567, 2003.
DOI : 10.1016/S0550-3213(03)00355-9

URL : https://hal.archives-ouvertes.fr/hal-00586662

J. Bouttier, P. D. Francesco, and E. Guitter, Planar maps as labeled mobiles, Electron. J. Combin, vol.11, issue.27, p.pp, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00586658

J. Bouttier and E. Guitter, Statistics of geodesics in large quadrangulations, Journal of Physics A: Mathematical and Theoretical, vol.41, issue.14, 2008.
DOI : 10.1088/1751-8113/41/14/145001

URL : https://hal.archives-ouvertes.fr/hal-00336781

J. Bouttier and E. Guitter, The three-point function of planar quadrangulations, Journal of Statistical Mechanics: Theory and Experiment, vol.2008, issue.07, 2008.
DOI : 10.1088/1742-5468/2008/07/P07020

URL : https://hal.archives-ouvertes.fr/hal-00336677

E. Brézin, C. Itzykson, G. Parisi, and J. B. , Planar diagrams, Communications in Mathematical Physics, vol.16, issue.1, pp.35-51, 1978.
DOI : 10.1007/BF01614153

G. Chapuy, Random permutations and their discrepancy process. AO- fA'07 (actes DMTCS), 2007.
URL : https://hal.archives-ouvertes.fr/hal-01184782

G. Chapuy, Are even maps on surfaces likely to be bipartite ? Fifth Colloquium on, Mathematics and Computer Science, 2008.

G. Chapuy, A new combinatorial identity for unicellular maps, via a direct bijective approach, International Conference FPSAC'09, 2009.
DOI : 10.1016/j.aam.2011.04.004

URL : https://hal.archives-ouvertes.fr/hal-01185440

G. Chapuy, Asymptotic Enumeration of Constellations and Related Families of Maps on Orientable Surfaces, Combinatorics, Probability and Computing, vol.18, issue.04
DOI : 10.1016/S0304-3975(02)00007-5

URL : https://hal.archives-ouvertes.fr/hal-00713483

G. Chapuy, The structure of unicellular maps, and a link between maps of positive genus and planar labelled trees. Probability Theory and Related Fields

G. Chapuy, E. Fusy, M. Kang, and B. Shoilekova, A complete grammar for decomposing a family of graphs into 3-connected components, Electronic Journal of Combinatorics, vol.15, p.148, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00713485

G. Chapuy, M. Marcus, and G. Schaeffer, On the number of rooted maps on orientable surfaces, 2007.

P. Chassaing and G. Schaeffer, Random planar lattices and integrated superBrownian excursion. Probab. Theory Related Fields, pp.161-212, 2004.
DOI : 10.1007/978-3-0348-8211-8_8

URL : https://hal.archives-ouvertes.fr/inria-00099448

R. Cori, S. Dulucq, and G. Viennot, Shuffle of parenthesis systems and baxter permutations, Journal of Combinatorial Theory, Series A, vol.43, issue.1, pp.1-22, 1986.
DOI : 10.1016/0097-3165(86)90018-X

R. Cori and B. Vauquelin, Planar maps are well labeled trees, Journal canadien de math??matiques, vol.33, issue.5, pp.1023-1042, 1981.
DOI : 10.4153/CJM-1981-078-2

M. D. Donsker, Justification and Extension of Doob's Heuristic Approach to the Kolmogorov- Smirnov Theorems, The Annals of Mathematical Statistics, vol.23, issue.2, pp.277-281, 1952.
DOI : 10.1214/aoms/1177729445

M. Drmota, Systems of functional equations Random Structures Algorithms Average-case analysis of algorithms (Dagstuhl, pp.103-124, 1995.

M. Drmota, O. Giménez, and M. Noy, Degree distribution in random planar graphs. en préparation
URL : https://hal.archives-ouvertes.fr/hal-01194677

P. Duchon, P. Flajolet, G. Louchard, and G. Schaeffer, Random generation of combinatorial structures: Boltzmann samplers and beyond, Proceedings of the 2011 Winter Simulation Conference (WSC), pp.577-625, 2004.
DOI : 10.1109/WSC.2011.6147745

URL : https://hal.archives-ouvertes.fr/hal-00654267

B. Duplantier, Conformal fractal geometry & boundary quantum gravity In Fractal geometry and applications : a jubilee of Beno??tBeno??t Mandelbrot, de Proc. Sympos. Pure Math, pp.365-482, 2004.

L. Euler, Solutio problematis ad geometriam situs pertinentis. Commentarii academiae scientiarum Petropolitanae, pp.128-140

P. Flajolet and A. Odlyzko, Singularity Analysis of Generating Functions, SIAM Journal on Discrete Mathematics, vol.3, issue.2, pp.216-240, 1990.
DOI : 10.1137/0403019

URL : https://hal.archives-ouvertes.fr/inria-00075725

P. Flajolet and R. Sedgewick, Analytic Combinatorics, 2009.
DOI : 10.1017/CBO9780511801655

URL : https://hal.archives-ouvertes.fr/inria-00072739

Z. Gao, The number of degree restricted maps on general surfaces, Discrete Mathematics, vol.123, issue.1-3, pp.47-63, 1993.
DOI : 10.1016/0012-365X(93)90006-F

Z. Gao, C. Nicholas, and . Wormald, Enumeration of Rooted Cubic Planar Maps, Annals of Combinatorics, vol.6, issue.3, pp.313-325, 2002.
DOI : 10.1007/s000260200006

J. Zhicheng, I. M. Gao, . Wanless, C. Nicholas, and . Wormald, Counting 5- connected planar triangulations, J. Graph Theory, vol.38, issue.1, pp.18-35, 2001.

O. Giménez and M. Noy, Asymptotic enumeration and limit laws of planar graphs, Journal of the American Mathematical Society, vol.22, issue.2, pp.309-329, 2009.
DOI : 10.1090/S0894-0347-08-00624-3

P. Ian, D. M. Goulden, and . Jackson, Combinatorial enumeration, 2004.

I. P. Goulden and D. M. Jackson, The KP hierarchy, branched covers, and triangulations, Advances in Mathematics, vol.219, issue.3, 2008.
DOI : 10.1016/j.aim.2008.06.013

A. Goupil and G. Schaeffer, FactoringN-Cycles and Counting Maps of Given Genus, European Journal of Combinatorics, vol.19, issue.7, pp.819-834, 1998.
DOI : 10.1006/eujc.1998.0215

J. Harer and D. Zagier, The Euler characteristic of the moduli space of curves, Inventiones Mathematicae, vol.57, issue.33, pp.457-485, 1986.
DOI : 10.1007/BF01390325

D. M. Jackson, Counting cycles in permutations by group characters, with an application to a topological problem, Transactions of the American Mathematical Society, vol.299, issue.2, pp.785-801, 1987.
DOI : 10.1090/S0002-9947-1987-0869231-9

D. M. Jackson, Some combinatorial problems associated with products of conjugacy classes of the symmetric group, Journal of Combinatorial Theory, Series A, vol.49, issue.2, pp.363-369, 1988.
DOI : 10.1016/0097-3165(88)90062-3

D. M. Jackson and T. I. , Visentin : A character-theoretic approach to embeddings of rooted maps in an orientable surface of given genus, Trans. Amer. Math. Soc, vol.322, issue.1, pp.343-363, 1990.

O. Kallenberg, Foundations of modern probability. Probability and its Applications, 1997.

V. G. Knizhnik, A. M. Polyakov, and A. B. , Zamolodchikov : Fractal structure of 2D-quantum gravity. Modern Phys, Lett. A, vol.3, issue.8, pp.819-826, 1988.

P. Steven and . Lalley, Finite range random walk on free groups and homogeneous trees, Ann. Probab, vol.21, issue.4, pp.2087-2130, 1993.

K. Sergei, . Lando, and K. Alexander, Zvonkin : Graphs on surfaces and their applications , volume 141 de Encyclopaedia of Mathematical Sciences, 2004.

J. Gall, The topological structure of scaling limits of large planar maps, Inventiones mathematicae, vol.15, issue.3, pp.621-670, 2007.
DOI : 10.1007/s00222-007-0059-9

J. François and L. Gall, Geodesics in large planar maps and in the brownian map, 2008.

J. Gall and F. Paulin, Scaling Limits of Bipartite Planar Maps are Homeomorphic to the 2-Sphere, Geometric and Functional Analysis, vol.18, issue.3, pp.893-918, 2008.
DOI : 10.1007/s00039-008-0671-x

J. Marckert and G. Miermont, Invariance principles for random bipartite planar maps, The Annals of Probability, vol.35, issue.5, pp.1642-1705, 2007.
DOI : 10.1214/009117906000000908

URL : https://hal.archives-ouvertes.fr/hal-00004645

J. Marckert and A. Mokkadem, Limit of normalized quadrangulations: The Brownian map, The Annals of Probability, vol.34, issue.6, pp.2144-2202, 2006.
DOI : 10.1214/009117906000000557

URL : https://hal.archives-ouvertes.fr/hal-00307498

M. Marcus and G. Schaeffer, Une bijection simple pour les cartes orientables, 2001.
URL : https://hal.archives-ouvertes.fr/inria-00100704

W. S. Massey, Algebraic topology : An introduction, 1967.

G. Miermont, On the sphericity of scaling limits of random planar quadrangulations, Electronic Communications in Probability, vol.13, issue.0, pp.248-257, 2008.
DOI : 10.1214/ECP.v13-1368

URL : https://hal.archives-ouvertes.fr/hal-00292487

G. Miermont and M. Weill, Radius and profile of random planar maps with faces of arbitrary degrees, Electronic Journal of Probability, vol.13, issue.0, pp.79-106, 2008.
DOI : 10.1214/EJP.v13-478

URL : https://hal.archives-ouvertes.fr/hal-00292074

B. Mohar and C. Thomassen, Graphs on surfaces Johns Hopkins Studies in the Mathematical Sciences, 2001.

R. C. Mullin, On the enumeration of tree-rooted maps. Canad, J. Math, vol.19, pp.174-183, 1967.

C. Pivoteau, B. Salvy-et-michèle-soria, and . Soria, Boltzmann oracle for combinatorial systems, Colloquium on Mathematics and Computer Science : Algorithms , Trees, Combinatorics and Probability, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00346845

D. Poulalhon and G. Schaeffer, Optimal Coding and Sampling of Triangulations, Algorithmica, vol.46, issue.3-4, pp.505-527, 2006.
DOI : 10.1007/s00453-006-0114-8

URL : https://hal.archives-ouvertes.fr/hal-00159287

J. Propp, Lattice structure for orientations of graphs, 1993.

J. Rémy, Un proc??d?? it??ratif de d??nombrement d'arbres binaires et son application ?? leur g??n??ration al??atoire, RAIRO. Informatique th??orique, vol.19, issue.2, pp.179-195, 1985.
DOI : 10.1051/ita/1985190201791

N. Robertson, D. Sanders, P. Seymour, and R. Thomas, The Four-Colour Theorem, Journal of Combinatorial Theory, Series B, vol.70, issue.1, pp.2-44, 1997.
DOI : 10.1006/jctb.1997.1750

N. Robertson and R. Vitray, Representativity of surface embeddings In Paths, flows, and VLSI-layout, Algorithms Combin, vol.9, pp.293-328, 1988.

G. Schaeffer, Bijective census and random generation of Eulerian planar maps with prescribed vertex degrees, Electron. J. Combin, vol.4, issue.14, p.pp, 1997.

G. Schaeffer, Conjugaison d'arbres et cartes combinatoires aléatoires, Thèse de doctorat, 1999.

G. Schaeffer and E. Vassilieva, A bijective proof of Jackson's formula for the number of factorizations of a cycle, Journal of Combinatorial Theory, Series A, vol.115, issue.6, pp.903-924, 2008.
DOI : 10.1016/j.jcta.2007.12.002

R. P. Stanley, de Cambridge Studies in Advanced Mathematics, Enumerative combinatorics, vol.1, issue.49, 1997.

R. P. Stanley, Enumerative combinatorics de Cambridge Studies in Advanced Mathematics, With a foreword by Gian-Carlo Rota and appendix 1 by Sergey Fomin, 1999.

. Gerard-t-'hooft, A planar diagram theory for strong interactions, Nucl. Phys. B, vol.72, 1974.

T. R. Walsh and A. B. Lehman, Counting rooted maps by Genus. I, Journal of Combinatorial Theory, Series B, vol.13, issue.3, pp.192-218, 1972.
DOI : 10.1016/0095-8956(72)90056-1

URL : http://doi.org/10.1016/0095-8956(72)90049-4

T. R. Walsh and A. B. Lehman, Counting rooted maps by Genus. I, Journal of Combinatorial Theory, Series B, vol.13, issue.3, pp.122-141, 1972.
DOI : 10.1016/0095-8956(72)90056-1

URL : http://doi.org/10.1016/0095-8956(72)90049-4

T. R. Walsh and A. B. Lehman, Counting rooted maps by genus III: Nonseparable maps, Journal of Combinatorial Theory, Series B, vol.18, issue.3, pp.222-259, 1975.
DOI : 10.1016/0095-8956(75)90050-7

URL : http://doi.org/10.1016/0095-8956(75)90050-7

H. Whitney, Congruent Graphs and the Connectivity of Graphs, American Journal of Mathematics, vol.54, issue.1, pp.150-168, 1932.
DOI : 10.2307/2371086

H. Whitney, 2-Isomorphic Graphs, American Journal of Mathematics, vol.55, issue.1/4, pp.245-254, 1933.
DOI : 10.2307/2371127

R. Alan and . Woods, Coloring rules for finite trees, and probability of monadic second order sentences. Random structures and algorithms, pp.453-485, 1997.

E. M. Wright, The number of connected sparsely edged graphs, Journal of Graph Theory, vol.65, issue.4, pp.317-330, 1977.
DOI : 10.1002/jgt.3190010407