D. Aldous, Asymptotic Fringe Distributions for General Families of Random Trees, The Annals of Applied Probability, vol.1, issue.2, pp.228-266, 1991.
DOI : 10.1214/aoap/1177005936

D. Aldous, B. Flannery, and J. L. Palacios, Two Applications of Urn Processes The Fringe Analysis of Search Trees and The Simulation of Quasi-Stationary Distributions of Markov Chains, Probability in the Engineering and Informational Sciences, pp.293-307, 1988.
DOI : 10.2307/3211876

K. B. Athreya and S. Karlin, Embedding of Urn Schemes into Continuous Time Markov Branching Processes and Related Limit Theorems, The Annals of Mathematical Statistics, vol.39, issue.6, pp.1801-1817, 1968.
DOI : 10.1214/aoms/1177698013

K. B. Athreya and P. E. Ney, Branching processes, Die Grundlehren der mathematischen Wissenschaften, 0196.
DOI : 10.1007/978-3-642-65371-1

R. A. Baeza-yates, Fringe analysis revisited, ACM Computing Surveys, vol.27, issue.1, pp.109-119, 1995.
DOI : 10.1145/214037.214103

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.45.3426

A. Bagchi and A. K. , Asymptotic Normality in the Generalized Polya???Eggenberger Urn Model, with an Application to Computer Data Structures, SIAM Journal on Algebraic Discrete Methods, vol.6, issue.3, pp.394-405, 1985.
DOI : 10.1137/0606041

C. Banderier, P. Flajolet, G. Schaeffer, and M. Soria, Random maps, coalescing saddles, singularity analysis, and Airy phenomena, Random Structures and Algorithms, vol.15, issue.3, pp.194-246, 2001.
DOI : 10.1002/rsa.10021

URL : https://hal.archives-ouvertes.fr/inria-00108014

R. J. Baxter, Exactly Solved Models in Statistical Mechanics, 1982.
DOI : 10.1142/9789814415255_0002

F. Bergeron, G. Labelle, and P. Leroux, Combinatorial species and tree-like structures, 1998.
DOI : 10.1017/CBO9781107325913

F. Bergeron, P. Flajolet, and B. Salvy, Varieties of increasing trees, Proceedings of the 17th Colloquium on Trees in Algebra and Programming, pp.92-116, 1992.
DOI : 10.1007/3-540-55251-0_2

URL : https://hal.archives-ouvertes.fr/inria-00074977

L. Norman and . Biggs, Algebraic graph theory, 1974.

H. William and . Burge, An analysis of a tree sorting method and some properties of a set of trees, First USA-JAPAN Computer Conference Proceedings, AFIPS and IPSJ, pp.372-378, 1972.

K. Chandrasekharan, Elliptic functions, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of, Mathematical Sciences], vol.281, 1985.

L. Cheno, P. Flajolet, J. Françon, C. Puech, and J. Vuillemin, Dynamic data structures: Finite files, limiting profiles and variance analysis, Eighteenth Annual Conference on Communication, Control, and Computing, pp.223-232, 1980.

E. Van, F. Conrad, and P. Flajolet, The Fermat cubic, elliptic functions, continued fractions, and a combinatorial excursion, Séminaire Lotharingien de Combinatoire, vol.54, issue.B54g, pp.1-44, 2006.

B. Daireaux, V. Maume-deschamps, and B. Vallée, The Lyapunov tortoise and the dyadic hare, International Conference on Analysis of Algorithms Discrete Mathematics & Theoretical Computer Science Proceedings, vol.AD, pp.71-94, 2005.
URL : https://hal.archives-ouvertes.fr/hal-01184044

. Frank and . Hollander, Large deviations, 2000.

A. Dixon, On the doubly periodic functions arising out of the curve x 3 + y 3 ? 3?xy = 1, The Quarterly Journal of Pure and Applied Mathematics, vol.24, pp.167-233, 1890.

D. Dumont, A combinatorial interpretation for the Schett recurrence on the Jacobian elliptic functions, Mathematics of Computation, vol.33, issue.148, pp.1293-1297, 1979.
DOI : 10.1090/S0025-5718-1979-0537974-1

M. Durand, Combinatoire analytique et algorithmique des ensembles de données, 2004.

A. Edelman and E. Kostlan, The road from Kac's matrix to Kac's random polynomials, Proceedings of the 1994 SIAM Applied Linear Algebra Conference SIAM, pp.503-507, 1994.

W. Feller, An introduction to probability theory and its applications, 1971.

P. Flajolet, Combinatorial aspects of continued fractions, Discrete Mathematics, vol.32, issue.3, pp.125-161, 1980.
DOI : 10.1016/0012-365X(80)90248-4

P. Flajolet and J. Françon, Structures de données dynamiques en reservoir borné, III Journées Algorithmiques, Proceedings of a meeting, 1980.

P. Flajolet, J. Gabarró, and H. Pekari, Analytic urns, The Annals of Probability, vol.33, issue.3, pp.1200-1233, 2005.
DOI : 10.1214/009117905000000026

P. Flajolet, L. Danì-ele-gardy, and . Thimonier, Birthday paradox, coupon collectors, caching algorithms and self-organizing search, Discrete Applied Mathematics, vol.39, issue.3, pp.207-229, 1992.
DOI : 10.1016/0166-218X(92)90177-C

URL : https://hal.archives-ouvertes.fr/inria-00075832

P. Flajolet, X. Gourdon, and C. Martínez, Patterns in random binary search trees, Random Structures and Algorithms, vol.11, issue.3, pp.223-244, 1997.
DOI : 10.1002/(SICI)1098-2418(199710)11:3<223::AID-RSA2>3.0.CO;2-2

URL : https://hal.archives-ouvertes.fr/inria-00073700

P. Flajolet and F. Guillemin, The formal theory of birth-and-death processes, lattice path combinatorics and continued fractions, Advances in Applied Probability, vol.41, issue.03, pp.750-778, 2000.
DOI : 10.1016/0012-365X(80)90248-4

URL : https://hal.archives-ouvertes.fr/inria-00073005

P. Flajolet and A. M. 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, P. Poblete, and A. Viola, On the Analysis of Linear Probing Hashing, Algorithmica, vol.22, issue.4, pp.490-515, 1998.
DOI : 10.1007/PL00009236

URL : https://hal.archives-ouvertes.fr/inria-00073424

P. Flajolet and V. Puyhaubert, Analytic combinatorics at OK Corral, 2005.

P. Flajolet and R. Sedgewick, Mellin transforms and asymptotics: Finite differences and Rice's integrals, Theoretical Computer Science, vol.144, issue.1-2, pp.101-124, 1995.
DOI : 10.1016/0304-3975(94)00281-M

URL : http://doi.org/10.1016/0304-3975(94)00281-m

P. Flajolet and M. Soria, General combinatorial schemas: Gaussian limit distributions and exponential tails, Discrete Mathematics, vol.114, issue.1-3, pp.159-180, 1993.
DOI : 10.1016/0012-365X(93)90364-Y

URL : https://hal.archives-ouvertes.fr/inria-00075557

J. Françon, G. Viennot, and J. Vuillemin, Description and analysis of an efficient priority queue representation, 19th Annual Symposium on Foundations of Computer Science (sfcs 1978), pp.1-7, 1978.
DOI : 10.1109/SFCS.1978.13

J. Françon and G. Viennot, Permutations selon leurs pics, creux, doubles mont??es et double descentes, nombres d'euler et nombres de Genocchi, Discrete Mathematics, vol.28, issue.1, pp.21-35, 1979.
DOI : 10.1016/0012-365X(79)90182-1

B. Friedman, A simple urn model, Communications on Pure and Applied Mathematics, vol.27, issue.1, pp.59-70, 1949.
DOI : 10.1002/cpa.3160020103

J. Gani, Random-allocation and urn models, Stochastic methods and their applications, pp.313-320, 2004.
DOI : 10.1093/imammb/10.1.51

URL : http://hdl.handle.net/1885/79535

A. Gnedin and J. Pitman, Exchangeable Gibbs partitions and Stirling triangles, Journal of Mathematical Sciences, vol.30, issue.11, 2004.
DOI : 10.1007/s10958-006-0335-z

URL : http://arxiv.org/abs/math/0412494

R. Gouet, A martingale approach to strong convergence in a generalized P??lya-Eggenberger urn model, Statistics & Probability Letters, vol.8, issue.3, pp.225-228, 1989.
DOI : 10.1016/0167-7152(89)90126-0

P. Ian, D. M. Goulden, and . Jackson, Combinatorial enumeration, Distributions, continued fractions, and the Ehrenfest urn model, pp.41-62, 1983.

I. Higueras, J. Moler, F. Plo, and M. , Urn models and differential algebraic equations, Journal of Applied Probability, vol.187, issue.02, pp.401-412, 2003.
DOI : 10.1214/aop/1176990853

URL : http://projecteuclid.org/download/pdfview_1/euclid.jap/1053003552

L. Holst, A unified approach to limit theorems for urn models, Journal of Applied Probability, vol.7, issue.01, pp.154-162, 1979.
DOI : 10.2307/3213276

F. M. Hoppe, P???lya-like urns and the Ewens' sampling formula, Journal of Mathematical Biology, vol.3, issue.1, pp.91-94, 1984.
DOI : 10.1007/BF00275863

Y. Itoh, On a ruin problem with interaction, Annals of the Institute of Statistical Mathematics, vol.54, issue.1, pp.635-641, 1973.
DOI : 10.1007/BF02479405

Y. Itoh, C. Mallows, and L. Shepp, Explicit sufficient invariants for an interacting particle system, Journal of Applied Probability, vol.103, issue.03, pp.633-641, 1998.
DOI : 10.2307/3213372

S. Janson, Functional limit theorems for multitype branching processes and generalized P??lya urns, Stochastic Processes and Applications, pp.177-245, 2004.
DOI : 10.1016/j.spa.2003.12.002

URL : http://doi.org/10.1016/j.spa.2003.12.002

L. Norman, S. Johnson, and . Kotz, Urn models and their application, 1977.

M. Kac, Random Walk and the Theory of Brownian Motion, The American Mathematical Monthly, vol.54, issue.7, pp.369-391, 1947.
DOI : 10.2307/2304386

S. Karlin and J. Mcgregor, Ehrenfest urn models, Journal of Applied Probability, vol.7, issue.02, pp.352-376, 1965.
DOI : 10.2140/pjm.1958.8.87

J. F. Kingman, Martingales in the Ok Corral, Martingales in the OK Corral, pp.601-606, 1999.
DOI : 10.1112/S0024609399006098

J. F. Kingman and S. E. Volkov, Solution to the OK Corral model via decoupling of Friedman's urn, Journal of Theoretical Probability, vol.16, issue.1, pp.267-276, 2003.
DOI : 10.1023/A:1022294908268

E. Donald and . Knuth, The art of computer programming, Sorting and Searching, 1998.

F. Valentin, B. A. Kolchin, V. P. Sevastyanov, and . Chistyakov, Random allocations, 1978.

S. Kotz and N. Balakrishnan, Advances in urn models during the past two decades Advances in combinatorial methods and applications to probability and statistics, Stat. Ind. Technol, vol.98, pp.203-257, 1997.

S. Kotz, H. Mahmoud, and P. Robert, On generalized P??lya urn models, Statistics & Probability Letters, vol.49, issue.2, pp.163-173, 2000.
DOI : 10.1016/S0167-7152(00)00045-6

P. Laplace, Théorie analytique des probabilités, II, ´ Editions Jacques Gabay, 1995.

P. Leroux and G. X. Viennot, Combinatorial resolution of systems of differential equations, I. Ordinary differential equations, Lecture Notes in Mathematics, vol.29, issue.6, pp.210-245, 1986.
DOI : 10.1016/0097-3165(80)90001-1

P. Lindqvist, Some remarkable sine and cosine functions, Ricerche di Matematica XLIV, issue.2, pp.269-290, 1995.

P. Lindqvist and J. Peetre, Two Remarkable Identities, Called Twos, for Inverses to Some Abelian Integrals, The American Mathematical Monthly, vol.108, issue.5, pp.403-410, 2001.
DOI : 10.2307/2695794

E. Lundberg, Om hypergoniometriskafunktioner af komplexa variabla, Manuscript, 1879, English translation On hypergoniometric functions of complex variables " available from Jaak Peetre's web page

A. J. Maciejewski, J. M. Ollagnier, A. Nowicki, and J. Strelcyn, Around Jouanolou non-integrability theorem, Indagationes Mathematicae, vol.11, issue.2, pp.239-254, 2000.
DOI : 10.1016/S0019-3577(00)89081-3

H. Mahmoud, On rotations in fringe-balanced binary trees, Information Processing Letters, vol.65, issue.1, pp.41-46, 1998.
DOI : 10.1016/S0020-0190(97)00184-1

B. Mohar, Some applications of Laplace eigenvalues of graphs, Graph Symmetry: Algebraic Methods and, NATO ASI Ser, pp.225-275, 1997.

A. Jean-moulin-ollagnier, J. Nowicki, and . Strelcyn, On the non-existence of constants of derivations: the proof of a theorem of Jouanolou and its development, Bulletin des Sciences Mathématiques, vol.119, issue.3, pp.195-233, 1995.

J. Donald, L. Newman, and . Shepp, The double dixie cup problem, American Mathematical Monthly, vol.67, pp.58-61, 1960.

A. Panholzer and H. Prodinger, An analytic approach for the analysis of rotations in fringe-balanced binary search trees, Annals of Combinatorics, vol.19, issue.2, pp.173-184, 1998.
DOI : 10.1007/BF01608487

J. Pitman, Combinatorial stochastic processes Lecture Notes for Saint-Flour Course, 2002.

N. Pouyanne, An algebraic approach of large Pólya processes, To appear in Annales de l'Institut Henri Poincaré, 40 pages

V. Puyhaubert, Modèles d'urnes et phénomènes de seuil en combinatoire analytique, 2005.

A. Schett, Properties of the Taylor series expansion coefficients of the Jacobian elliptic functions, Mathematics of Computation, vol.30, issue.133, pp.143-147, 1976.
DOI : 10.1090/S0025-5718-1976-0391477-3

R. Sedgewick and P. Flajolet, An introduction to the analysis of algorithms, 1996.

N. J. Sloane, The On-Line Encyclopedia of Integer Sequences, 2006.
DOI : 10.1007/978-3-540-73086-6_12

R. T. Smythe, Central limit theorems for urn models, Stochastic Process, Appl, vol.65, issue.1, pp.115-137, 1996.

R. P. Stanley, Enumerative combinatorics, 1986.

E. C. Titchmarsh, The theory of functions, 1939.

G. Viennot, Une interpretation combinatoire des coefficients des développements en sérieentì ere des fonctions elliptiques de Jacobi, Journal of Combinatorial Theory, series A, pp.29-121, 1980.

J. S. Vitter and P. Flajolet, Analysis of algorithms and data structures, Handbook of Theoretical Computer Science, Algorithms and Complexity, vol.A, pp.431-524, 1990.

J. Vuillemin, A unifying look at data structures, Communications of the ACM, vol.23, issue.4, pp.229-239, 1980.
DOI : 10.1145/358841.358852

E. T. Whittaker and G. N. Watson, A course of modern analysis, 1927.

D. Williams, Probability with martingales, Cambridge Mathematical Textbooks, 1991.

D. Williams and P. Mcilroy, The OK Corral and the power of the law (a curious Poisson-kernel formula for a parabolic equation), The Bulletin of the, pp.166-170, 1998.

A. C. and C. Yao, On random 2?3 trees, Acta Informatica, vol.1, issue.2, pp.159-170, 1978.
DOI : 10.1007/BF00289075

V. M. Zolotarev, One-dimensional stable distributions, Translated from the Russian by H. H. McFaden, 1986.