Large deviations of Markov chains indexed by random trees
Dembo, Amir ; Mörters, Peter ; Sheffield, Scott
Annales de l'I.H.P. Probabilités et statistiques, Tome 41 (2005), p. 971-996 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{AIHPB_2005__41_6_971_0,
     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},
     volume = {41},
     year = {2005},
     pages = {971-996},
     doi = {10.1016/j.anihpb.2004.09.005},
     mrnumber = {2172206},
     zbl = {1078.60020},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_2005__41_6_971_0}
}

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) pp. 971-996. doi : 10.1016/j.anihpb.2004.09.005. http://gdmltest.u-ga.fr/item/AIHPB_2005__41_6_971_0/

[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 1166406 | Zbl 0791.60008

[2] K.B. Athreya, P.E. Ney, Branching Processes, Springer, New York, 1972. | MR 373040 | Zbl 0259.60002

[3] I. Benjamini, Y. Peres, Markov chains indexed by trees, Ann. Probab. 22 (1994) 219-243. | MR 1258875 | Zbl 0793.60080

[4] A. Dembo, O. Zeitouni, Large Deviations Techniques and Applications, Springer, New York, 1998. | MR 1619036 | Zbl 0896.60013

[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 1894069 | Zbl 0996.60110

[6] R. Durrett, Probability: Theory and Examples, Duxbury Press, Belmont, CA, 1996. | MR 1609153

[7] M. Dwass, The total progeny in a branching process and a related random walk, J. Appl. Probab. 6 (1969) 682-686. | MR 253433 | Zbl 0192.54401

[8] H.O. Georgii, Gibbs Measures and Phase Transitions, de Gruyter, Berlin, 1988. | MR 956646 | Zbl 0657.60122

[9] P. Jagers, Branching Processes with Biological Applications, Wiley, London, 1975. | MR 488341 | Zbl 0356.60039

[10] O. Kallenberg, Stability of critical cluster fields, Math. Nachr. 77 (1977) 7-43. | MR 443078 | Zbl 0361.60058

[11] D.P. Kennedy, The Galton-Watson process conditioned on the total progeny, J. Appl. Probab. 12 (1975) 800-806. | MR 386042 | Zbl 0322.60072

[12] W. König, P. Mörters, Brownian intersection local times: upper tails and thick points, Ann. Probab. 30 (2002) 1605-1656. | MR 1944002 | Zbl 1032.60073

[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 1703137 | Zbl 0945.60039

[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 1336708 | Zbl 0819.60077

[15] A. Meir, J.W. Moon, On the altitude of nodes in random trees, Canad. J. Math. 30 (1978) 997-1015. | MR 506256 | Zbl 0394.05015

[16] R. Otter, The multiplicative process, Ann. Math. Statist. 20 (1949) 206-224. | MR 30716 | Zbl 0033.38301

[17] R. Pemantle, Tree-indexed processes, Statist. Sci. 10 (2) (1995) 200-231. | MR 1368099 | Zbl 0955.60528