Large deviations of Markov chains indexed by random trees
Annales de l'I.H.P. Probabilités et statistiques, Tome 41 (2005) no. 6, pp. 971-996. 
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     author = {Dembo, Amir and M\"orters, Peter and Sheffield, Scott},
     title = {Large deviations of {Markov} chains indexed by random trees},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {971--996},
     publisher = {Elsevier},
     volume = {41},
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     zbl = {1078.60020},
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     url = {http://archive.numdam.org/articles/10.1016/j.anihpb.2004.09.005/}
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Dembo, Amir; Mörters, Peter; Sheffield, Scott. Large deviations of Markov chains indexed by random trees. Annales de l'I.H.P. Probabilités et statistiques, Tome 41 (2005) no. 6, pp. 971-996. doi : 10.1016/j.anihpb.2004.09.005. http://archive.numdam.org/articles/10.1016/j.anihpb.2004.09.005/

[1] D. Aldous, The continuum random tree II: An overview, in: Stochastic Analysis, Proc. Symp., Durham/UK 1990, London Math. Soc. Lecture Note Ser., vol. 167, 1991, pp. 23-70. | MR | Zbl

[2] K.B. Athreya, P.E. Ney, Branching Processes, Springer, New York, 1972. | MR | Zbl

[3] I. Benjamini, Y. Peres, Markov chains indexed by trees, Ann. Probab. 22 (1994) 219-243. | MR | Zbl

[4] A. Dembo, O. Zeitouni, Large Deviations Techniques and Applications, Springer, New York, 1998. | MR | Zbl

[5] A. Dembo, N. Gantert, Y. Peres, O. Zeitouni, Large deviations for random walks on Galton-Watson trees: averaging and uncertainty, Probab. Theory Related Fields 122 (2002) 241-288. | MR | Zbl

[6] R. Durrett, Probability: Theory and Examples, Duxbury Press, Belmont, CA, 1996. | MR

[7] M. Dwass, The total progeny in a branching process and a related random walk, J. Appl. Probab. 6 (1969) 682-686. | MR | Zbl

[8] H.O. Georgii, Gibbs Measures and Phase Transitions, de Gruyter, Berlin, 1988. | MR | Zbl

[9] P. Jagers, Branching Processes with Biological Applications, Wiley, London, 1975. | MR | Zbl

[10] O. Kallenberg, Stability of critical cluster fields, Math. Nachr. 77 (1977) 7-43. | MR | Zbl

[11] D.P. Kennedy, The Galton-Watson process conditioned on the total progeny, J. Appl. Probab. 12 (1975) 800-806. | MR | Zbl

[12] W. König, P. Mörters, Brownian intersection local times: upper tails and thick points, Ann. Probab. 30 (2002) 1605-1656. | MR | Zbl

[13] J.-F. Le Gall, The Hausdorff measure of the range of super-Brownian motion, in: Bramson M., Durrett R. (Eds.), Perplexing Problems in Probability, Birkhäuser, Basel, 1999, pp. 285-314. | MR | Zbl

[14] R. Lyons, R. Pemantle, Y. Peres, Ergodic theory on Galton-Watson trees: speed of random walk and dimension of harmonic measure, Ergodic Theory Dynam. Systems 15 (1995) 593-619. | MR | Zbl

[15] A. Meir, J.W. Moon, On the altitude of nodes in random trees, Canad. J. Math. 30 (1978) 997-1015. | MR | Zbl

[16] R. Otter, The multiplicative process, Ann. Math. Statist. 20 (1949) 206-224. | MR | Zbl

[17] R. Pemantle, Tree-indexed processes, Statist. Sci. 10 (2) (1995) 200-231. | MR | Zbl

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