C. , .. , S. Galton-watson-process, and .. , 176 4.2.1 Reduction to a Bernoulli source 177 4.2.3 Reduction to a skeleton 178 4.2.4 A binary search tree, p.186

D. Aldous, Brownian excursions, critical random graphs and the multiplicative coalescent, The Annals of Probability, vol.25, issue.2, pp.812-854, 1997.
DOI : 10.1214/aop/1024404421

J. David and . Aldous, Stochastic Models and Descriptive Statistics for Phylogenetic Trees, from Yule to Today, Statistical Science, vol.16, issue.1, pp.23-34, 2001.

B. Krishna, P. E. Athreya, and . Ney, Branching processes, Die Grundlehren der mathematischen Wissenschaften

J. M. David-aldous and . Steele, The Objective Method: Probabilistic Combinatorial Optimization and Local Weak Convergence, Probability on discrete structures, pp.1-72, 2004.

A. Ash, Information theory. Interscience Tracts in Pure and Applied Mathematics, 1965.

A. Barabási and R. Albert, Emergence of Scaling in Random Networks, Science, vol.286, issue.5439, pp.509-512, 1999.

. Bar90, . Héì, and . Barcelo, On the action of the symmetric group on the Free Lie algebra and the partition lattice, J. Combin. Theory Ser. A, vol.55, issue.1, pp.93-129, 1990.

[. Baccelli and B. Blaszczyszyn, Stochastic Geometry and Wireless Networks, Volume I -Theory, volume 1 of Foundations and Trends in Networking Stochastic Geometry and Wireless Networks, Volume II -Applications; see http, pp.3-4, 2009.

A. Edward, E. R. Bender, and . Canfield, The asymptotic number of labeled graphs with given degree sequences, J. Combinatorial Theory Ser. A, vol.24, issue.3, pp.296-307, 1978.

[. Bassino, J. Clément, and C. Nicaud, The standard factorization of Lyndon words: an average point of view, Discrete Mathematics, vol.290, issue.1, pp.1-25, 2005.
DOI : 10.1016/j.disc.2004.11.002

URL : https://hal.archives-ouvertes.fr/hal-00619337

N. Broutin and L. Devroye, An Analysis of the Height of Tries with Random Weights on the Edges, Combinatorics, Probability and Computing, vol.7, issue.02, pp.161-202, 2007.
DOI : 10.1214/aoms/1177729330

]. J. Big76 and . Biggins, The first-and last-birth problems for a multitype age-dependent branching process Advances in Appl, Probability, vol.8, issue.3, pp.446-459, 1976.

]. J. Big77 and . Biggins, Chernoff's Theorem in the branching random walk, J. Appl. Probability, vol.14, issue.3, pp.630-636, 1977.

[. Bollobás, S. Janson, and O. Riordan, The phase transition in inhomogeneous random graphs. Random Structures Algorithms, pp.3-122, 2007.

M. [. Balakrishnan and . Koutras, Runs and scans with applications. Wiley Series in Probability and Statistics, 2002.

[. Bohman, The triangle-free process, Advances in Mathematics, vol.221, issue.5, pp.1653-1677, 2009.
DOI : 10.1016/j.aim.2009.02.018

[. Bollobás and O. Riordan, Constrained graph processes, Electron. J. Combin, vol.7, issue.20, 2000.

I. Benjamini and O. Schramm, Recurrence of distributional limits of finite planar graphs, Electron. J. Probab, vol.6, issue.13, p.pp, 2001.

F. [. Brands, R. J. Steutel, and . Wilms, On the number of maxima in a discrete sample, Statistics & Probability Letters, vol.20, issue.3, pp.209-217, 1994.
DOI : 10.1016/0167-7152(94)90044-2

[. Bhamidi, R. Van-der-hofstad, and J. S. Van-leeuwaarden, Scaling Limits for Critical Inhomogeneous Random Graphs with Finite Third Moments, Electronic Journal of Probability, vol.15, issue.0, pp.1682-1703, 2010.
DOI : 10.1214/EJP.v15-817

S. [. Bahadur, Large Deviations of the Sample Mean in General Vector Spaces, The Annals of Probability, vol.7, issue.4, pp.587-621, 1979.
DOI : 10.1214/aop/1176994985

P. Chassaing and E. Azad, Asymptotic behavior of some factorizations of random words. arXiv preprint, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00475379

P. Chassaing and P. Flajolet, Hachage, arbres, chemins & graphes, Gaz. Math, issue.95, pp.29-49, 2003.

[. Chauvin, T. Klein, J. Marckert, and A. Rouault, Martingales and Profile of Binary Search Trees, Electronic Journal of Probability, vol.10, issue.0, pp.420-435, 2005.
DOI : 10.1214/EJP.v10-257

URL : https://hal.archives-ouvertes.fr/hal-00138808

P. Chassaing and J. Marckert, Parking functions , empirical processes, and the width of rooted labeled trees, Electron. J. Combin, vol.8, issue.19, p.pp, 2001.

A. [. Chauvin and . Rouault, Connecting Yule process, Bisection and Binary Search Tree via martingales, J. Iranian Statistical Society, vol.3, pp.88-116, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00138806

]. L. Dev86 and . Devroye, A Note on the Height of Binary Search Trees, Journal of the ACM (JACM), vol.33, issue.3, pp.489-498, 1986.

L. Devroye, A Limit Theory for Random Skip Lists, The Annals of Applied Probability, vol.2, issue.3, pp.597-609, 1992.
DOI : 10.1214/aoap/1177005651

A. Dembo and A. Montanari, Gibbs measures and phase transitions on sparse random graphs, Brazilian Journal of Probability and Statistics, vol.24, issue.2, pp.137-211, 2010.
DOI : 10.1214/09-BJPS027

]. M. Drm01 and . Drmota, An analytic approach to the height of binary search trees Average-case analysis of algorithms, Algorithmica, vol.29, issue.12, pp.89-119, 1998.

F. [. Drossel and . Schwabl, Self-organized critical forest-fire model, Physical Review Letters, vol.40, issue.11, pp.1629-1632, 1992.
DOI : 10.1103/PhysRevB.40.7425

N. Stewart, T. G. Ethier, and . Kurtz, Markov Processes: Characterization and Convergence John Wiley and sons, 1986. [ER59] P. Erd? os and A. Rényi. On random graphs, I. Publ. Math. Debrecen, vol.6, pp.290-297, 1959.

[. Erd?-os and A. Rényi, On the evolution of random graphs, Publications of the Mathematical Institute of the Hungarian Academy of Sciences, pp.17-31, 1960.

P. Erd?-os, S. Suen, and P. Winkler, On the size of a random maximal graph, Random Structures & Algorithms, vol.1, issue.2, pp.309-318, 1995.
DOI : 10.1017/S0963548300000183

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

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

]. E. Gil59 and . Gilbert, Random graphs, Ann. Math. Statist, vol.30, pp.1141-1144, 1959.

[. Giladi and J. B. Keller, Eulerian Number Asymptotics, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.445, issue.1924, pp.291-303, 1924.
DOI : 10.1098/rspa.1994.0062

T. E. Harris, The Theory of Branching Processes, Die Grundlehren der Mathematischen Wissenschaften, p.119
DOI : 10.1007/978-3-642-51866-9

R. Hardy and S. C. Harris, A Spine Approach to Branching Diffusions with Applications to L p -Convergence of Martingales, Séminaire de Probabilités XLII, pp.281-330, 2009.
DOI : 10.1007/978-3-642-01763-6_11

C. Hohlweg and C. Reutenauer, Lyndon words, permutations and trees, Theoretical Computer Science, vol.307, issue.1, pp.173-178, 2003.
DOI : 10.1016/S0304-3975(03)00099-9

URL : https://doi.org/10.1016/s0304-3975(03)00099-9

[. Janson, T. Luczak, and A. Rucinski, Random Graphs. Wiley-Interscience Series in Discrete Mathematics and Optimization, 2000.

A. Joseph, The component sizes of a critical random graph with given degree sequence. The Annals of Applied Probability, pp.2560-2594

]. J. Kin75 and . Kingman, The first birth problem for an age-dependent branching process, Ann. Probability, vol.3, issue.5, pp.790-801, 1975.

J. Gall, Itô's excursion theory and random trees. Stochastic Process, Appl, vol.120, issue.5, pp.721-749, 2010.

]. M. Lot97 and . Lothaire, Combinatorics on words. Cambridge Mathematical Library, 1997.

B. D. Mckay, Asymptotics for symmetric 0-1 matrices with prescribed row sums, Ars Combin, vol.19, issue.A, pp.15-25, 1985.

M. Molloy, B. Reednew51, and ]. J. Newburgh, A critical point for random graphs with a given degree sequence Random Graphs '93 The variation of spectra. Duke Math, Proceedings of the Sixth International Seminar on Random Graphs and Probabilistic Methods in Combinatorics and Computer Science, pp.161-179165, 1951.

[. Norros and H. Reittu, On a conditionally Poissonian graph process, Advances in Applied Probability, vol.4, issue.01, pp.59-7561, 1984.
DOI : 10.1103/RevModPhys.74.47

B. Pittel, Note on the heights of random recursive trees and random m-ary search trees, Random Structures & Algorithms, vol.33, issue.2, pp.337-347, 1994.
DOI : 10.1007/BF00265991

B. Reed, The height of a random binary search tree, Journal of the ACM, vol.50, issue.3, pp.306-332, 2003.
DOI : 10.1145/765568.765571

I. Matthew and . Roberts, Almost sure asymptotics for the random binary search tree, 21st International Meeting on Probabilistic , Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), Discrete Math. Theor. Comput

N. [. Ruci´nskiruci´nski and . Wormald, Random Graph Processes with Degree Restrictions, Combinatorics, Probability and Computing, vol.41, issue.02, pp.169-180, 1992.
DOI : 10.1016/0196-6774(90)90029-E

B. Söderberg, General formalism for inhomogeneous random graphs, Physical Review E, vol.64, issue.6, p.66121, 2002.
DOI : 10.1103/PhysRevE.64.026118

R. Sedgewick and P. Flajolet, An Introduction to the Analysis of Algorithms, 1996.

J. Spencer, Enumerating graphs and Brownian motion, Communications on Pure and Applied Mathematics, vol.50, issue.3, pp.291-294, 1997.
DOI : 10.1002/(SICI)1097-0312(199703)50:3<291::AID-CPA4>3.0.CO;2-6

F. [. Sawada and . Ruskey, Generating Lyndon brackets., Journal of Algorithms, vol.46, issue.1, pp.21-26, 2003.
DOI : 10.1016/S0196-6774(02)00286-9

K. Subramanian, R. Siromoney, L. Mathewtan73, and ]. S. Tanny, Lyndon trees, Theoretical Computer Science, vol.106, issue.2, pp.373-383717, 1973.
DOI : 10.1016/0304-3975(92)90259-I

URL : https://doi.org/10.1016/0304-3975(92)90259-i

S. Tatyana and . Turova, Phase Transitions in Dynamical Random Graphs, J. Stat. Phys, vol.123, issue.5, pp.1007-1032, 2006.

S. Tatyana and . Turova, Diffusion approximation for the components in critical inhomogeneous random graphs of rank 1. Random Structures Algorithms, pp.486-539, 2013.