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20. B. Bercu, D. Chafaï. Modélisation stochastique et simulation : cours et applications. Sciences
sup. (Dunod, Paris, 2007). Série « Mathématiques appliquées pour le Master / SMAI ».
21. J. Berstel, D. Perrin, C. Reutenauer, Codes and Automata (Encyclopedia of Mathematics and
Its Applications), 1st edn. (Cambridge University Press, New York, 2009)
22. J. Bertoin, Random Fragmentation and Coagulation Processes. Cambridge Studies in
Advanced Mathematics (Cambridge University Press, Cambridge, 2006)
23. P. Biane, J. Pitman, M. Yor, Probability laws related to the Jacobi theta and Riemann zeta
functions, and Brownian excursions. Bull. Am. Math. Soc. 38, 435–465 (2001)
24. J. Biggins, Chernoff’s theorem in the branching random walk. J. Appl. Probab. 14, 630–636
(1977)
25. J.D. Biggins, Martingale convergence in the branching random walk. Adv. Appl. Probab. 10,
62–84 (1978)
26. J.D. Biggins, Uniform convergence of martingales in the branching random walk. Ann.
Probab. 20(1), 137–151 (1992)
27. J.D. Biggins, How fast does a general branching random walk spread? in Classical and
Modern Branching Processes. The IMA Volumes in Mathematics and Its Applications, vol.
84, ed. by K.B. Athreya, P. Jagers (Springer, New York, 1997), pp. 19–39
28. P. Billingsley, Probability and Measure, 3rd edn. Wiley Series in Probability and
Mathematical Statistics (Wiley, New York, 1995). A Wiley-Interscience Publication.
29. D. Blackwell, D. Kendall, The Martin boundary for Pólya’s urn and an application to
stochastic population growth. J. Appl. Probab. 1(2), 284–296 (1964)
30. B. Bollobas, I. Simon, Repeated random insertion into a priority queue. J. Algoritm. 6,
466–477 (1985)
31. N. Broutin, L. Devroye, E. McLeish, M. De la Salle, The height of increasing trees. Random
Struct. Algoritm. 32, 494–518 (2008)
32. J. Capetanakis, Tree algorithms for packet broadcast channels. IEEE Trans. Inf. Theory
IT-25:505–515 (1979)
33. E. Cesaratto, B. Vallée. Gaussian distribution of trie depth for strongly tame sources. Comb.
Probab. Comput. 24(1), 54–103 (2015)
34. P. Chassaing, P. Flajolet, Hachage, arbres, chemins et graphes. Gaz. Math. 95, 29–49 (2003)
35. P. Chassaing, J.-F. Marckert, Parking functions, empirical processes and the width of rooted
labeled trees. Electron. J. Comb. 8, R14 (2001)
36. B. Chauvin, N. Pouyanne, m-ary search trees when m > 26: a strong asymptotics for the
space requirements. Random Struct. Algoritm. 24(2), 133–154 (2004)
37. B. Chauvin, M. Drmota, J. Jabbour-Hattab, The profile of binary search trees. Ann. Appl.
Probab. 11, 1042–1062 (2001)
38. B. Chauvin, P. Flajolet, D. Gardy, B. Gittenberger, And/or trees revisited. Comb. Probab.
Comput. 13(4–5), 475–497 (2004)
39. B. Chauvin, T. Klein, J.-F. Marckert, A. Rouault, Martingales and profile of binary search
trees. Electron. J. Probab. 10, 420–435 (2005)
40. B. Chauvin, N. Pouyanne, R. Sahnoun, Limit distributions for large Pólya urns. Ann. Appl.
Probab. 21(1), 1–32 (2011)
41. B. Chauvin, D. Gardy, C. Mailler, A sprouting tree model for random boolean functions.
Random Struct. Algoritm. 47(4), 635–662 (2015)
42. B. Chauvin, C. Mailler, N. Pouyanne, Smoothing equations for large Pólya urns. J. Theor.
Probab. 28, 923–957 (2015)
43. B. Chauvin, D. Gardy, N. Pouyanne, D.-H. Ton That, B-urns. Lat. Am. J. Probab. Math. Stat.
13, 605–634 (2016)
44. H.-H. Chern, M. Fuchs, H.-K. Hwang, Phase changes in random point quadtrees. ACM
Trans. Algorithms 3(Issue 2), Art. 12 (2007)
45. J. Clément, P. Flajolet, B. Vallée, The analysis of hybrid trie structures, in Proceedings of the
Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, San Francisco, 25–27 January
1998, pp. 531–539
Bibliographie
20. B. Bercu, D. Chafaï. Modélisation stochastique et simulation : cours et applications. Sciences
sup. (Dunod, Paris, 2007). Série « Mathématiques appliquées pour le Master / SMAI ».
21. J. Berstel, D. Perrin, C. Reutenauer, Codes and Automata (Encyclopedia of Mathematics and
Its Applications), 1st edn. (Cambridge University Press, New York, 2009)
22. J. Bertoin, Random Fragmentation and Coagulation Processes. Cambridge Studies in
Advanced Mathematics (Cambridge University Press, Cambridge, 2006)
23. P. Biane, J. Pitman, M. Yor, Probability laws related to the Jacobi theta and Riemann zeta
functions, and Brownian excursions. Bull. Am. Math. Soc. 38, 435–465 (2001)
24. J. Biggins, Chernoff’s theorem in the branching random walk. J. Appl. Probab. 14, 630–636
(1977)
25. J.D. Biggins, Martingale convergence in the branching random walk. Adv. Appl. Probab. 10,
62–84 (1978)
26. J.D. Biggins, Uniform convergence of martingales in the branching random walk. Ann.
Probab. 20(1), 137–151 (1992)
27. J.D. Biggins, How fast does a general branching random walk spread? in Classical and
Modern Branching Processes. The IMA Volumes in Mathematics and Its Applications, vol.
84, ed. by K.B. Athreya, P. Jagers (Springer, New York, 1997), pp. 19–39
28. P. Billingsley, Probability and Measure, 3rd edn. Wiley Series in Probability and
Mathematical Statistics (Wiley, New York, 1995). A Wiley-Interscience Publication.
29. D. Blackwell, D. Kendall, The Martin boundary for Pólya’s urn and an application to
stochastic population growth. J. Appl. Probab. 1(2), 284–296 (1964)
30. B. Bollobas, I. Simon, Repeated random insertion into a priority queue. J. Algoritm. 6,
466–477 (1985)
31. N. Broutin, L. Devroye, E. McLeish, M. De la Salle, The height of increasing trees. Random
Struct. Algoritm. 32, 494–518 (2008)
32. J. Capetanakis, Tree algorithms for packet broadcast channels. IEEE Trans. Inf. Theory
IT-25:505–515 (1979)
33. E. Cesaratto, B. Vallée. Gaussian distribution of trie depth for strongly tame sources. Comb.
Probab. Comput. 24(1), 54–103 (2015)
34. P. Chassaing, P. Flajolet, Hachage, arbres, chemins et graphes. Gaz. Math. 95, 29–49 (2003)
35. P. Chassaing, J.-F. Marckert, Parking functions, empirical processes and the width of rooted
labeled trees. Electron. J. Comb. 8, R14 (2001)
36. B. Chauvin, N. Pouyanne, m-ary search trees when m > 26: a strong asymptotics for the
space requirements. Random Struct. Algoritm. 24(2), 133–154 (2004)
37. B. Chauvin, M. Drmota, J. Jabbour-Hattab, The profile of binary search trees. Ann. Appl.
Probab. 11, 1042–1062 (2001)
38. B. Chauvin, P. Flajolet, D. Gardy, B. Gittenberger, And/or trees revisited. Comb. Probab.
Comput. 13(4–5), 475–497 (2004)
39. B. Chauvin, T. Klein, J.-F. Marckert, A. Rouault, Martingales and profile of binary search
trees. Electron. J. Probab. 10, 420–435 (2005)
40. B. Chauvin, N. Pouyanne, R. Sahnoun, Limit distributions for large Pólya urns. Ann. Appl.
Probab. 21(1), 1–32 (2011)
41. B. Chauvin, D. Gardy, C. Mailler, A sprouting tree model for random boolean functions.
Random Struct. Algoritm. 47(4), 635–662 (2015)
42. B. Chauvin, C. Mailler, N. Pouyanne, Smoothing equations for large Pólya urns. J. Theor.
Probab. 28, 923–957 (2015)
43. B. Chauvin, D. Gardy, N. Pouyanne, D.-H. Ton That, B-urns. Lat. Am. J. Probab. Math. Stat.
13, 605–634 (2016)
44. H.-H. Chern, M. Fuchs, H.-K. Hwang, Phase changes in random point quadtrees. ACM
Trans. Algorithms 3(Issue 2), Art. 12 (2007)
45. J. Clément, P. Flajolet, B. Vallée, The analysis of hybrid trie structures, in Proceedings of the
Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, San Francisco, 25–27 January
1998, pp. 531–539