, Un critère dû à Dynkin fournit une condition suffisante sur la fonction

, Lois d'Ewens Suggestions bibliographiques

, Ce bref chapitre fournit quelques suggestions de lecture, nécessairement incomplètes et subjectives, concernant les probabilités de niveau master. Parmi les ouvrages les plus accessibles, on peut citer notamment le livre classique et incontournable de William Feller

, Les martingales à temps discret constituent le sujet principal des livres de Jacques Neveu

, Les chaînes de Markov à temps et espace discrets constituent le sujet principal des livres de Paoli Baldi, Laurent Mazliak

J. Celui-de and . Norris, Nor98b] aborde également les processus de Markov à temps continu et espace d'états dénombrable ainsi que les martingales. Citons aussi les ouvrages de Michel Benaïm et Nicole El Karoui [BEK05], Jean-François Delmas et Benjamin Jourdain [DJ06], Étienne Pardoux [Par07], et Thierry Bodineau [Bod14] qui présentent également des applications importantes ou classiques (physique, biologie, mathématiques financières, etc). Dans cette veine, avec également un pont vers l'épreuve de modélisation de l'agrégation de mathématiques

L. 'ouvrage-de and C. Cocozza-thivent, CT97] présente des applications des probabilités à la fiabilité. La théorie des valeurs extrêmes est abordée par exemple dans le livre de Paul Embrechts, Claudia Klüppelberg

F. Gall,

R. Albert and A. , Barabási-« Emergence of scaling in random networks, Science, vol.214, issue.286, pp.509-512, 1999.

A. , Rev. Modern Phys, vol.74, issue.1, pp.47-97, 2002.

. C. Abc-+-00, S. Ané, D. Blachère, P. Chafaï, I. Fougères et al., Scheffer-Sur les inégalités de Sobolev logarithmiques, Panoramas et Synthèses, vol.10, p.344, 2000.

A. L. Addario-berry and B. A. , Reed-« Ballot theorems, Horizons of combinatorics, Bolyai Soc. Math. Stud, vol.17, pp.9-35, 2008.

A. R. Arratia, A. D. Barbour, and S. Tavaré, Logarithmic combinatorial structures : a probabilistic approach, European Mathematical Society (EMS), 0199.
DOI : 10.4171/000

. G. Acg-+-99, P. Ausiello, G. Crescenzi, V. Gambosi, A. Kann et al., Combinatorial optimization problems and their approximability properties, Protasi-Complexity and approximation, p.278, 1999.

D. J. Aldous and J. , Fill-« Reversible Markov Chains and Random Walks on Graphs », cours non publié disponible sous forme électronique sur Internet, vol.17, p.38, 1994.
DOI : 10.1007/bf01048272

. Ag13a,

A. Asselah and A. , Gaudillière-« From logarithmic to subdiffusive polynomial fluctuations for internal dla and related growth models, The Annals of Probability, vol.41, issue.3A, pp.1115-1159, 2013.
DOI : 10.1214/12-aop762

URL : https://doi.org/10.1214/12-aop762

. Ag13b, Sublogarithmic fluctuations for internal dla, vol.41, pp.1160-1179, 2013.

A. G. Anderson and A. Guionnet, Zeitouni-An introduction to random matrices, Cambridge Studies in Advanced Mathematics, vol.118, p.296, 2010.
DOI : 10.1017/cbo9780511801334

URL : http://www.wisdom.weizmann.ac.il/%7Ezeitouni/cupbook.pdf

A. A. Littérature, J. E. Aho, and J. Hopcroft, Ullman-The design and analysis of computer algorithms, ries in Computer Science and Information Processing, vol.278, p.90, 1975.

D. Aldous and W. , Krebs-« The "birth-and-assassination" process », Statist. Probab. Lett, vol.10, issue.5, pp.427-430, 1990.
DOI : 10.1016/0167-7152(90)90024-2

URL : http://www.stat.berkeley.edu/~aldous/Papers/me44.pdf

. Ald85,

D. J. , Aldous-« Exchangeability and related topics », École d'été de probabilités de Saint-Flour, XIII-1983, Lecture Notes in Math, vol.1117, pp.1-198, 0199.

. Ald91, Threshold limits for cover times, vol.4, pp.197-211, 1991.

A. K. Athreya and P. E. , Ney-Branching processes, vol.0373040, p.243, 2004.

. And87,

D. André-«, Sleep-« Uniform random generation of balanced parenthesis strings, Solution directe du problème résolu par M. Bertrand, vol.105, pp.122-128, 1887.

. S. Asm00, Asmussen-Ruin probabilities, Advanced Series on Statistical Science & Applied Probability, vol.2, p.252, 2000.

. Bak94,

D. Bakry-«-l, hypercontractivité et son utilisation en théorie des semigroupes, Lectures on probability theory, vol.1581, pp.1-114, 1992.

. R. Bas95, Bass-Probabilistic techniques in analysis, Probability and its Applications, p.325, 1995.

. Bax82,

R. J. Baxter, Exactly solved models in statistical mechanics, vol.81, p.3, 1982.

F. Baccelli and P. , Palm martingale calculus and stochastic recurrences, Stochastic Modelling and Applied Probability, Applications of Mathematics, vol.26, p.3, 2003.

C. Biernacki, Chrétien-« Degeneracy in the maximum likelihood estimation of univariate Gaussian mixtures with EM, Statist. Probab. Lett, vol.61, issue.4, p.7, 2003.

B. Bercu, Chafaï-Modélisation stochastique et simulation, cours et applications, Collection Sciences Sup, Dunod, Mathématiques appliquées/SMAI. 81, 91, vol.103, p.377, 2007.

B. P. Brockwell and R. A. , Davis-Introduction to time series and forecasting, second éd, Springer Texts in Statistics, p.103, 2002.

B. V. Bansaye, J. Delmas, L. Marsalle, and V. C. Tran, Limit theorems for Markov processes indexed by continuous time GaltonWatson trees, vol.21, pp.2263-2314, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00431118

D. Bakry, Émery-« Diffusions hypercontractives, vol.84, pp.177-206, 1983.

M. Benaïm and N. E. Karoui, Promenade aléatoire : chaînes de markov et simulations ; martingales et stratégies, Mathématiques appliquées, Les éd. de l'École polytechnique, vol.215, p.377, 2005.

. C. Ber76, Berge-Graphs and hypergraphs, revised éd

. American, , vol.6, p.67, 1976.

. J. Ber06, Bertoin-Random fragmentation and coagulation processes, Cambridge Studies in Advanced Mathematics, vol.102, p.243, 2006.

. Ber09, Berestycki-Recent progress in coalescent theory, Ensaios Matemáticos, Mathematical Surveys, vol.16, p.199, 2009.

B. D. Bakry, I. Gentil, and M. Ledoux, Analysis and geometry of Markov diffusion operators, Grundlehren der Mathematischen Wissenschaften, vol.348, p.344, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00929960

. R. Bha97 and . Bhatia, Matrix analysis, vol.169, p.296, 1997.

B. A. Barbour and L. Holst, Janson-Poisson approximation, Oxford Studies in Probability, vol.2, p.15, 1992.

B. N. Bouleau, Lépingle-Numerical methods for stochastic processes, Wiley Series in Probability and Mathematical Statistics : Applied Probability and Statistics, p.376, 1994.

P. Barbe and M. Ledoux-probabilités, De la licence à l'agrégation, p.377, 1998.

B. P. Baldi, L. Mazliak, P. Priouret-martingales, and . Chaînes-de-markov, Théorie élémentaire et exercices corrigés, BMR14. S. Bubeck, E. Mossel et M. Z. Rácz-« On the influence of the seed graph in the preferential attachment model, p.215, 2008.

. T. Bod14 and . Bodineau-«, Promenade aléatoire : chaînes de Markov et martingales, Cours de l'École Polytechnique, vol.81, p.377, 2014.

. Bol80, Bollobás-« A probabilistic proof of an asymptotic formula for the number of labelled regular graphs, European J. Combin, vol.1, issue.4, pp.311-316, 1980.

. E. Bol89, Bolthausen-« A note on the diffusion of directed polymers in a random environment, Comm. Math. Phys, vol.123, issue.4, pp.529-534, 1989.

L. Bor95,

V. S. , Borkar-Probability theory, p.377, 1995.

. C. Bor08 and . Bordenave-«, On the birth-and-assassination process, with an application to scotching a rumor in a network, Electron. J. Probab, vol.13, issue.66, p.304, 2008.

. C. Bor14a, Bordenave-« Lecture notes on random graphs and probabilistic combinatorial optimization », Disponible sur la page Internet de l'auteur, vol.67, p.278, 2014.

. Bor14b, A short course on random matrices, p.296, 2014.

B. C. Bouzitat, G. Pagès, and F. , Petit et F. Carrance-En passant par hasard.. . les probabilités de tous les jours, Vuibert, vol.16, p.11, 1999.

M. Benaïm, Raimond-« Self-interacting diffusions IV : Rate of convergence, Electron. J. Probab, vol.16, issue.66, pp.1815-1843, 2011.

. P. Bré99, Gibbs fields, Monte Carlo simulation, and queues, Texts in Applied Mathematics, vol.31, p.377, 1999.

B. B. Bollobás, O. Riordan, and J. Spencer, Tusnády-« The degree sequence of a scale-free random graph process, Random Structures Algorithms, vol.18, issue.3, p.10, 2001.

Z. Bai and J. W. , Silverstein-Spectral analysis of large dimensional random matrices, second éd, Springer Series in Statistics, p.296, 2010.

B. N. Berestycki and O. Schramm, Zeitouni-« Mixing times for random k-cycles and coalescence-fragmentation chains, Ann. Probab, vol.39, issue.5, p.95, 2011.

V. Bally and D. Talay-«, The Euler scheme for stochastic differential equations : error analysis with Malliavin calculus, Probabilités numériques, vol.38, p.376, 1992.

. Cap12,

M. , Capitaine-« Introduction aux grandes matrices aléatoires », Disponible sur la page Internet de l'auteur, p.296, 2012.

. O. Cat99 and . Catoni-«, Simulated annealing algorithms and Markov chains with rare transitions, Séminaire de Probabilités, XXXIII, vol.1709, pp.69-119, 1999.

A. Charpentier, Denuit-Mathématiques de l'assurance nonvie-concepts fondamentaux de théorie du risque, p.252, 2004.

C. N. Curien, T. Duquesne, and I. , Kortchemski et I. Manolescu-« Scaling limits and influence of the seed graph in preferential attachment trees, p.215, 2014.

D. Chafaï, Y. Doumerc, and F. Malrieu, Processus des restaurants chinois et loi d'ewens, vol.123, pp.56-74, 0198.

C. P. Caputo, P. Dai-pra, and G. Posta, Fuchs-« On the distribution of values of sums of random variables, Convex entropy decay via the Bochner-Bakry-Emery approach, vol.45, p.37, 1951.

P. Carmona and Y. Hu-«, On the partition function of a directed polymer in a Gaussian random environment, Probab. Theory Related Fields, vol.124, issue.3, pp.431-457, 2002.

. Cha06,

D. Chafaï-«-binomial, ESAIM Probab. Stat, vol.10, p.155, 2006.

. Cha13, Introduction aux matrices aléatoires, vol.296, pp.87-122, 2013.

. B. Clo13, Cloez-« Comportement asymptotique de processus avec sauts et applications pour des modèles avec branchement, p.243, 2013.

C. D. Chafaï, F. Malrieu, and K. Paroux-«, On the long time behavior of the TCP window size process, 242 CSY03. F. Comets, T. Shiga et N. Yoshida-« Directed polymers in a random environment : path localization and strong disorder, vol.8, p.6, 1997.

F. Comets, V. Vargas, and -. Lat, Majorizing multiplicative cascades for directed polymers in random media, Modern Birkhäuser Classics, vol.2, p.377, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00128291

F. Comets, Yoshida-« Directed polymers in random environment are diffusive at weak disorder, Ann. Probab, vol.34, issue.5, pp.1746-1770, 2006.

. B. Dav90, Davis-« Reinforced random walk, Probab. Theory Related Fields, vol.84, issue.2, pp.203-229, 1990.

D. , Dacunha-Castelle et M. Duflo-Probabilités et statistiques

, Problèmes à temps mobile, Collection Mathématiques Appliquées pour la Maîtrise. [Collection of Applied Mathematics for the Master's Degree, vol.2, p.102, 1983.

H. Duminil-copin and S. Smirnov-«, The connective constant of the honeycomb lattice equals 2 + ? 2, Ann. of Math, vol.229, issue.2, pp.1653-1665, 2012.

. A. Dem05, Dembo-« Favorite points, cover times and fractals, Lectures on probability theory and statistics, vol.1869, pp.1-101, 2005.

.. L. Littérature-dev12, Devroye-« Simulating size-constrained Galton-Watson trees », SIAM J. Comput, vol.41, issue.1, p.91, 2012.

P. Diaconis and W. Fulton-«, A growth model, a game, an algebra, Lagrange inversion, and characteristic classes, Commutative algebra and algebraic geometry, vol.49, p.91, 1990.

D. V. Dumas, F. Guillemin, and P. Robert-«, A Markovian analysis of additive-increase multiplicative-decrease algorithms, Adv. in Appl. Probab, vol.34, issue.1, pp.85-111, 2002.

D. J. and -. Delmas, Applications aux sciences de l'ingénieur et du vivant, Jourdain-Modèles aléatoires, Mathématiques & Applications (Berlin) [Mathematics & Applications], vol.57, p.377, 2006.

D. B. Delyon and M. Lavielle, Moulines-« Convergence of a stochastic approximation version of the EM algorithm, Ann. Statist, vol.27, issue.1, pp.94-128, 1999.

D. A. Dempster, N. M. Laird, and D. B. , Rubin-« Maximum likelihood from incomplete data via the EM algorithm, J. Roy. Statist. Soc. Ser. B, vol.39, issue.1, p.47, 1977.

A. Dvoretzky, Motzkin-« A problem of arrangements, Duke Math. J, vol.14, p.80, 1947.

C. Dellacherie and P. Meyer, Probabilités et potentiel. Chapitres V à VIII, revised éd., Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics, vol.1385, p.377, 1980.

D. P. Diaconis, E. Mayer-wolf, O. Zeitouni, and M. P. , Zerner-« The Poisson-Dirichlet law is the unique invariant distribution for uniform split-merge transformations, Ann. Probab, vol.32, issue.1B, pp.915-938, 2004.

D. A. Doumas and V. G. , Papanicolaou-« Asymptotics of the rising moments for the coupon collector's problem », Electron. J. Probab, vol.18, issue.41, p.16, 2013.

. Drm09, Drmota-Random trees, SpringerWienNewYork, Vienna, 2009, An interplay between combinatorics and probability, p.68

P. Diaconis, Shahshahani-« Generating a random permutation with random transpositions, Z. Wahrsch. Verw. Gebiete, vol.57, issue.2, pp.159-179, 1981.

D. P. Doyle and J. , Snell-Random walks and electric networks, Carus Mathematical Monographs, vol.22, p.37, 1984.

P. Diaconis and M. Shahshahani-«, Time to reach stationarity in the Bernoulli-Laplace diffusion model, SIAM J. Math. Anal, vol.18, issue.1, pp.208-218, 1987.

D. M. Disertori, C. Sabot, and P. Tarrès-«-transience, , p.215, 2014.

. M. Duf97 and . Duflo, Translated from the 1990 French original by Stephen S. Wilson and revised by the author, Random iterative models, Applications of Mathematics, vol.34, 1997.

. R. Dur64, Durstenfeld-« Algorithm 235 : Random permutation, Communications of the ACM, vol.7, p.66, 1964.

. R. Dur08, Durrett-Probability models for DNA sequence evolution, second éd, Probability and its Applications, vol.172, p.199, 2008.

. R. Dur10a, Durrett-Probability : theory and examples, fourth éd, Cambridge Series in Statistical and Probabilistic Mathematics, p.377, 2010.

. Dur10b, Random graph dynamics, Cambridge Series in Statistical and Probabilistic Mathematics, p.215, 2010.

. Dwa69,

M. Dwass-«, The total progeny in a branching process and a related random walk. », J. Appl. Probability, vol.6, pp.682-686, 1969.

A. Dembo, Zeitouni-Large deviations techniques and applications, Stochastic Modelling and Applied Probability, vol.38, p.377, 2010.

P. Erd?s, T. Gallai-«-gráfok-el?írt-fokszámú-pontokkal, ». , and M. Lapok, Wiley Series in Probability and Mathematical Statistics : Probability and Mathematical Statistics, p.375, 1960.

E. P. Embrechts and C. Klüppelberg, Mikosch-Modelling extremal events, Applications of Mathematics, vol.33, p.377, 1997.

R. Erban and H. , Othmer-« From individual to collective behavior in bacterial chemotaxis, SIAM J. Appl. Math, vol.65, issue.2, p.313, 2004.

P. Erd?s and A. , Rényi-« On random graphs. I », Publ. Math. Debrecen, vol.6, pp.290-297, 1959.

. Er61a, On a classical problem of probability theory, Magyar Tud. Akad. Mat. Kutató Int. Közl, vol.6, pp.215-220, 1961.

. Er61b, On the evolution of random graphs, vol.38, pp.343-347, 1961.

. Ewe04,

W. J. , Ewens-Mathematical population genetics. I, second éd, Theoretical introduction, vol.27, p.199, 2004.

. W. Fel68, Feller-An introduction to probability theory and its applications, vol.I, p.377, 1968.

. Fel71, An introduction to probability theory and its applications, vol.II, p.377, 1971.

. T. Fer89, Ferguson-« Who solved the secretary problem ?, Statist. Sci, vol.4, issue.3, p.138, 1989.

D. Foata and A. Fuchs, Processus stochastiques : processus de poisson, chaînes de markov et martingales, Collection Sciences Sup, Dunod, p.252, 2004.

. J. Fil98, Fill-« An interruptible algorithm for perfect sampling via Markov chains, Ann. Appl. Probab, vol.8, issue.1, pp.131-162, 1998.

F. C. Fortuin, P. W. Kasteleyn, and J. , Ginibre-« Correlation inequalities on some partially ordered sets, Comm. Math. Phys, vol.22, pp.89-103, 1971.

. D. Fre65, -. Freedman, and . Friedman, 91 FY48. R. A. Fisher et F. Yates-Statistical Tables for Biological, vol.36, pp.956-970, 1948.

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

J. Glimm and A. , A functional integral point of view, p.37, 1987.

C. Graham and P. Robert-«, A multi-class mean-field model with graph structure for TCP flows », Progress in industrial mathematics at ECMI, Math. Ind, vol.15, pp.125-131, 2008.

. Gri99, Grimmett-Percolation, second éd, Grundlehren der Mathematischen Wissenschaften, vol.321, p.229, 1999.

. Gri10, Probability on graphs, vol.1, p.229, 2010.

G. F. Guillemin and P. Robert, Zwart-« AIMD algorithms and exponential functionals, Ann. Appl. Probab, vol.14, issue.1, pp.90-117, 2004.

?. G¯-ihman and A. V. , Skorohod-Stochastic differential equations, Ergebnisse der Mathematik und ihrer Grenzgebiete, vol.72, p.375, 1972.

G. C. Givens and R. M. , Shortt-« A class of Wasserstein metrics for probability distributions, Michigan Math. J, vol.31, issue.2, pp.231-240, 1984.

G. G. Grimmett and D. R. , Stirzaker-Probability and random processes, third éd, p.155, 2001.

C. Graham, Talay-Stochastic simulation and Monte Carlo methods, Stochastic Modelling and Applied Probability, vol.68, p.378, 2013.

. A. Gut13, Gut-Probability : a graduate course, second éd, Springer Texts in Statistics, p.377, 2013.

. O. Häg02, Häggström-Finite markov chains and algorithmic applications, vol.81, p.377, 2002.

. T. Har60, Harris-« A lower bound for the critical probability in a certain percolation process, Proc. Cambridge Philos. Soc, vol.56, pp.13-20, 1960.

. Har02, The theory of branching processes, vol.54, p.243, 2002.

. W. Has70, Hastings-« Monte Carlo sampling methods using Markov chains and their applications, Biometrika, issue.57, pp.97-109, 1970.

P. Hall and C. C. , Heyde-Martingale limit theory and its application, Probability and Mathematical Statistics, vol.91, p.377, 1980.

O. Häggström and J. , Jonasson-« Uniqueness and non-uniqueness in percolation theory, Probab. Surv, vol.3, pp.289-344, 2006.

H. R. Horn and C. R. , Johnson-Matrix analysis, second éd, p.296, 2013.

H. P. Haccou, P. Jagers, and V. A. , Vatutin-Branching processes : variation, growth, and extinction of populations, Cambridge Studies in Adaptive Dynamics, p.54, 2007.

. L. Hol01, Holst-« Extreme value distributions for random coupon collector and birthday problems, vol.4, pp.129-145, 2001.

. F. Hop84, Hoppe-« Pólya-like urns and the Ewens' sampling formula, J. Math. Biol, vol.20, issue.1, pp.91-94, 0199.

. L. Hör67, Hörmander-« Hypoelliptic second order differential equations, Acta Math, vol.119, p.10, 1967.

S. Herrmann and P. , Vallois-« From persistent random walk to the telegraph noise, Stoch. Dyn, vol.10, issue.2, pp.161-196, 2010.

I. J. , Imbrie et T. Spencer-« Diffusion of directed polymers in a random environment, J. Statist. Phys, vol.52, issue.3-4, pp.609-626, 1988.

J. N. Johnson and S. Kotz, An approach to modern discrete probability theory, Wiley Series in Probability and Mathematical Statistics, p.214, 1977.

J. N. Johnson and S. Kotz, Balakrishnan-Discrete multivariate distributions, Wiley Series in Probability and Statistics : Applied Probability and Statistics, 0199.

D. Jerison, L. Levine, and S. Sheffield-«, Logarithmic fluctuations for internal DLA, J. Amer. Math. Soc, vol.25, issue.1, pp.271-301, 2012.

J. D. Jerison, L. Levine, and S. Sheffield-«, Internal dla in higher dimensions, Electron. J. Probab, vol.18, pp.1-14, 2013.

J. Jacod, Protter-L'essentiel en théorie des probabilités, Enseignement des mathématiques, Cassini, p.377, 2002.

J. , Probability essentials, second éd, vol.377, 2003.

. Kac47,

M. Kac-«, Random walk and the theory of Brownian motion, Amer. Math. Monthly, vol.54, pp.369-391, 1947.

. Kac74, Reprinting of an article published in 1956, Papers arising from a Conference on Stochastic Differential Equations, vol.4, p.313, 1972.

S. Kotz and N. Balakrishnan-«, Advances in urn models during the past two decades, Advances in combinatorial methods and applications to probability and statistics, vol.214, pp.203-257, 1997.

. Kes80,

H. , Kesten-« The critical probability of bond percolation on the square lattice equals 1

, Comm. Math. Phys, vol.74, issue.1, pp.41-59, 1980.

. J. Kin80, Kingman-Mathematics of genetic diversity, CBMS-NSF Regional Conference Series in Applied Mathematics, vol.34, p.199, 1980.

. Kin93, Poisson processes, vol.3, p.199, 1993.

E. Kuhn, Lavielle-« Coupling a stochastic approximation version of EM with an MCMC procedure, ESAIM Probab. Stat, vol.8, p.112, 2004.

. D. Knu05, Knuth-The art of computer programming, vol.1, p.68, 2005.

. I. Kor15 and . Kortchemski, Predator-Prey Dynamics on Infinite Trees : A Branching Random Walk Approach, p.303, 2015.

K. P. Kloeden, Platen-« Numerical methods for stochastic differential equations », Nonlinear dynamics and stochastic mechanics, CRC Math. Model. Ser, vol.376, pp.437-461, 1995.

K. A. Krieger and M. Pollak, Samuel-Cahn-« Beat the mean : sequential selection by better than average rules, J. Appl. Probab, vol.45, issue.1, pp.244-259, 2008.
DOI : 10.1017/s0021900200004095

H. Kesten and B. P. , Stigum-« A limit theorem for multidimensional Galton-Watson processes, Ann. Math. Statist, vol.37, pp.1211-1223, 1966.
DOI : 10.1214/aoms/1177699266

URL : https://doi.org/10.1214/aoms/1177699266

K. J. Kemeny and J. , Reprinting of the 1960 original, Undergraduate Texts in Mathematics, vol.127, 1976.

I. Karatzas and S. E. , Shreve-Brownian motion and stochastic calculus, second éd, Graduate Texts in Mathematics, vol.113, p.378, 1991.

. Lac10,

H. , Lacoin-« New bounds for the free energy of directed polymers in dimension 1 + 1 and 1 + 2 », Comm. Math. Phys, vol.294, issue.2, pp.471-503, 2010.

. G. Law13, Lawler-Intersections of random walks, Modern Birkhäuser Classics, vol.37, 2013.

L. G. Lawler and M. Bramson, Griffeath-« Internal diffusion limited aggregation, Ann. Probab, vol.20, issue.4, pp.2117-2140, 1992.
DOI : 10.1214/aop/1176989542

URL : https://doi.org/10.1214/aop/1176989542

L. J. and -. Gall, Mouvement brownien, martingales et calcul stochastique, Mathématiques & Applications (Berlin), vol.71, p.377, 2013.

. T. Lig85, Liggett-Interacting particle systems, Grundlehren der Mathematischen Wissenschaften, Fundamental Principles of Mathematical Sciences, vol.276, p.265, 1985.

L. G. Lawler, Limic-Random walk : a modern introduction, Cambridge Studies in Advanced Mathematics, vol.123, p.37, 2010.
DOI : 10.1017/cbo9780511750854

URL : http://www.math.uchicago.edu/~lawler/srwbook.pdf

R. Lyons and Y. , Peres-Probability on trees and networks, p.68, 2015.
DOI : 10.1017/9781316672815

URL : http://mypage.iu.edu/~rdlyons/prbtree/book.pdf

L. D. Levin, Y. Peres, and E. L. , Wilmer-Markov chains and mixing times, vol.17, p.377, 2009.
DOI : 10.1090/mbk/058

Q. Liu and F. , Watbled-« Exponential inequalities for martingales and asymptotic properties of the free energy of directed polymers in a random environment, Stochastic Process. Appl, vol.119, issue.10, pp.3101-3132, 2009.

. Lé08, Probabilistic methods in statistical physics », Lecture notes-Tsinghua University, 0229.

. H. Mah09, Mahmoud-Pólya urn models, Texts in Statistical Science Series, p.214, 2009.

-. J. Mar04, Marckert-« Structures arborescentes, algorithmes », Habilitation à diriger des recherches, p.55, 2004.

.. A. Littérature-mau03, Maurer-« A bound on the deviation probability for sums of nonnegative random variables, JIPAM. J. Inequal. Pure Appl. Math, vol.4, issue.1, p.138, 2003.

. C. Mcd89 and . Mcdiarmid-«, On the method of bounded differences, London Math. Soc. Lecture Note Ser, vol.141, pp.148-188, 1989.

.. -. Mcd98 and . Concentration, Probabilistic methods for algorithmic discrete mathematics, vol.16, pp.195-248, 1998.

. T. Mik09, Mikosch-Non-life insurance mathematics, second éd, vol.252, 2009.

M. Mézard and A. , Montanari-Information, physics, and computation, Oxford Graduate Texts, p.277, 2009.

P. Mörters and Y. , Peres-Brownian motion, Cambridge Series in Statistical and Probabilistic Mathematics, p.325, 2010.

R. Motwani and P. Raghavan, Randomized algorithms, vol.16, p.66, 1995.

. N. Mrr-+-53, A. Metropolis, M. Rosenbluth, and A. Rosenbluth, Teller et E. Teller-« Equations of State Calculations by Fast Computing Machines », Journal of Chemical Physics, issue.21, pp.1087-1092, 1953.

S. Méléard, Villemonais-« Quasi-stationary distributions and population processes, Probab. Surv, vol.9, pp.340-410, 2012.

M. B. Mckay and N. , Wormald-« Uniform generation of random regular graphs of moderate degree, J. Algorithms, vol.11, issue.1, pp.52-67, 1990.

. S. Mé13, Méléard-« Modèles aléatoires en ecologie et evolution », Cours de l'École Polytechnique, vol.185, p.199, 2013.

. E. Nel67, Nelson-Dynamical theories of Brownian motion, p.358, 1967.

. J. Nev72, Neveu-Martingales à temps discret, Masson et Cie, éditeurs, p.377, 1972.

. J. Nev75, Neveu-Discrete-parameter martingales, revised éd

. American, , vol.10, p.377, 1975.

. J. Nor98a, Norris-Markov chains, Cambridge Series in Statistical and Probabilistic Mathematics, vol.2, p.252, 1997.

. J. Nor98b, Norris-Markov chains, vol.377, p.60, 1998.

D. J. Newman and L. Shepp-«, Alt-« Models of dispersal in biological systems, Amer. Math. Monthly, vol.67, issue.3, p.8, 1960.

T. J. Ott and J. H. , Kemperman-« Transient behavior of processes in the TCP paradigm, Probab. Engrg. Inform. Sci, vol.22, issue.3, pp.431-471, 2008.

. B. Øks03, Øksendal-Stochastic differential equations, sixth éd, Universitext, p.377, 2003.

. E. Par07 and . Pardoux, Processus de Markov et applications, Collection Sciences Sup, Dunod, 2007, Mathématiques appliquées/SMAI. 81, vol.102, p.377

. R. Pem07, Pemantle-« A survey of random processes with reinforcement, vol.214, p.215, 2007.

. Per07, Perthame-Transport equations in biology, Frontiers in Mathematics, p.243, 2007.

. J. Pit06 and . Pitman, Combinatorial stochastic processes, Lectures from the 32nd Summer School on Probability Theory, vol.1875, p.199, 2002.

. J. Pre00 and . Preater, Wilson-« Exact sampling with coupled Markov chains and applications to statistical mechanics, Sequential selection with a better-than-average rule, vol.50, p.81, 1996.

, Rev97. D. Revuz-Probabilités, p.377, 1997.

. P. Rob00 and . Robert, Réseaux et files d'attente : méthodes probabilistes, Mathématiques & Applications (Berlin) [Mathematics & Applications, vol.35, p.375, 2000.

. Rob05, Réseaux de communication, algorithmes et probabilités », Cours de l'École Polytechnique, p.242, 2005.

. Rob10, Mathématiques et réseau de communication », Dossiers pour la science (2010) hal:inria-00472217, p.242, 2010.

. Roy99,

G. Royer, RRS05. S. Robin, F. Rodolphe et S. Schbath-DNA, words and models, vol.5, p.102, 1999.

. W. Rud87, Rudin-Real and complex analysis, third éd, p.325, 1987.

, Issues de l'épreuve de modélisation de l'agrégation, Mathématiques en situation, SCOPOS, vol.11, 2001.

R. L. Rogers and D. Williams-diffusions, Markov processes, and martingales, vol.1, p.378, 1994.

D. Revuz, Yor-Continuous martingales and Brownian motion, third éd, Grundlehren der Mathematischen Wissenschaften, vol.293, p.377, 1999.

-. J. Ré85, Rémy-« Un procédé itératif de dénombrement d'arbres binaires et son application à leur génération aléatoire, R.A.I.R.O. Informatique Théorique, vol.19, issue.2, pp.179-195, 1985.

. S. She07 and . Sheffield-«, Gaussian free fields for mathematicians, Probab. Theory Related Fields, vol.139, issue.3-4, pp.521-541, 2007.

. A. Shi96, Shiryaev-Probability, second éd, Graduate Texts in Mathematics, vol.95, p.2, 1980.

J. Siltaneva, Mäkinen-« A comparison of random binary tree generators, The Computer Journal, vol.45, issue.6, pp.653-660, 2002.

. F. Spi70 and . Spitzer, Principes des cheminements aléatoires, Traduit de l'anglais par E, Baverez et J.-L. Guignard. Centre Interarmés de Recherche Opérationnelle, vol.2, p.37, 1970.

. Sta83,

A. J. , Stam-« Generation of a random partition of a finite set by an urn model, J. Combin. Theory Ser. A, vol.35, issue.2, pp.231-240, 1983.

. J. Ste94, Steele-« Le Cam's inequality and Poisson approximations, Amer. Math. Monthly, vol.101, issue.1, pp.48-54, 1994.

. Ste97, CBMS-NSF Regional Conference Series in Applied Mathematics, vol.69, p.277, 1997.

. Tal96,

D. Talay-«, Probabilistic numerical methods for partial differential equations : elements of analysis », Probabilistic models for nonlinear partial differential equations, Lecture Notes in Math, vol.1627, pp.148-196, 1995.

.. -. Tal02 and . Stochastic, Hamiltonian systems : exponential convergence to the invariant measure, and discretization by the implicit Euler scheme, Markov Process. Related Fields, vol.8, p.358, 2001.

. Tar11, Tarrès-« Localization of reinforced random walks, p.215, 2011.

. S. Tav04 and . Tavaré-«, Ancestral inference in population genetics, Lectures on probability theory and statistics, vol.1837, p.199, 2004.

. P. Tou99, Toulouse-Thèmes de probabilités et statistique, Dunod, p.377, 1999.

T. J. Tsitsiklis and C. H. Papadimitriou, Humblet-« The performance of a precedence-based queueing discipline, J. Assoc. Comput. Mach, vol.33, issue.3, p.90, 1986.

D. Talay and L. Tubaro-«, Expansion of the global error for numerical schemes solving stochastic differential equations, Stochastic Anal. Appl, vol.8, issue.4, p.376, 1990.
URL : https://hal.archives-ouvertes.fr/inria-00075490

T. A. Tripathi, S. Venugopalan, and D. B. , West-« A short constructive proof of the Erd?s-Gallai characterization of graphic lists, Lecture notes available on Internet, vol.67, issue.4, p.229, 2010.

. C. Vil03, Villani-Topics in optimal transportation, Graduate Studies in Mathematics, vol.58, p.243, 2003.

.. -. Vil06 and . Hypocoercive, International Congress of Mathematicians, vol.III, pp.473-498, 2006.

.. -. Vil08, «. H-theorem, and . Beyond, Boltzmann's entropy in today's mathematics », Boltzmann's legacy, ESI, Lect. Math. Phys, vol.359, pp.129-143, 2008.

.. -. Vil09 and . Hypocoercivity, Mem. Amer. Math. Soc, vol.202, issue.950, pp.141-358, 2009.

. Wil91,

D. Williams, Probability with martingales, Cambridge Mathematical Textbooks, vol.102, p.377, 1991.

. D. Wil96, Wilson-« Generating random spanning trees more quickly than the cover time, Proceedings of the 28'th annual ACM symposium on Theory of computing pages, p.68, 1996.

F. Wang, D. P. Landau, and -. Efficient, Multiple-Range Random Walk Algorithm to Calculate the Density of States, Physical Review Letters, vol.86, p.81, 2001.

. Yca02, Ycart-Modèles et algorithmes markoviens, Mathématiques & Applications (Berlin) [Mathematics & Applications], vol.39, p.325, 2002.

. J. Yuk98, Yukich-Probability theory of classical Euclidean optimization problems, Lecture Notes in Mathematics, vol.1675, p.277, 1998.