Annealed upper tails for the energy of a charged polymer
Annales de l'I.H.P. Probabilités et statistiques, Volume 47 (2011) no. 1, p. 80-110

We study the upper tails for the energy of a randomly charged symmetric and transient random walk. We assume that only charges on the same site interact pairwise. We consider annealed estimates, that is when we average over both randomness, in dimension three or more. We obtain a large deviation principle, and an explicit rate function for a large class of charge distributions.

Nous étudions les grandes déviations pour l'énergie d'un polymère. L'espace est discret, et le polymère est une chaine linéaire de n monomères associés à des charges. Nous supposons que deux charges n'intéragissent que lorsqu'elles occupent le même site de ℤd. Nous considérons le cas où les deux aléas, valeurs des charges et positions des monomères, sont moyennés, et où la dimension de l'espace est 3 ou plus. Nous obtenons un principe de grande déviations, et pour certaines distributions de charges, la fonctionnelle de taux est explicite.

DOI : https://doi.org/10.1214/09-AIHP355
Classification:  60K35,  82C22,  60J25
Keywords: random polymer, large deviations, random walk in random scenery, self-intersection local times
@article{AIHPB_2011__47_1_80_0,
     author = {Asselah, Amine},
     title = {Annealed upper tails for the energy of a charged polymer},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {47},
     number = {1},
     year = {2011},
     pages = {80-110},
     doi = {10.1214/09-AIHP355},
     zbl = {1229.60105},
     mrnumber = {2779398},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2011__47_1_80_0}
}
Asselah, Amine. Annealed upper tails for the energy of a charged polymer. Annales de l'I.H.P. Probabilités et statistiques, Volume 47 (2011) no. 1, pp. 80-110. doi : 10.1214/09-AIHP355. http://www.numdam.org/item/AIHPB_2011__47_1_80_0/

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