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

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.

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.

DOI : 10.1214/09-AIHP355
Classification : 60K35, 82C22, 60J25
Mots-clés : 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},
     pages = {80--110},
     publisher = {Gauthier-Villars},
     volume = {47},
     number = {1},
     year = {2011},
     doi = {10.1214/09-AIHP355},
     mrnumber = {2779398},
     zbl = {1229.60105},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1214/09-AIHP355/}
}
TY  - JOUR
AU  - Asselah, Amine
TI  - Annealed upper tails for the energy of a charged polymer
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 2011
SP  - 80
EP  - 110
VL  - 47
IS  - 1
PB  - Gauthier-Villars
UR  - http://archive.numdam.org/articles/10.1214/09-AIHP355/
DO  - 10.1214/09-AIHP355
LA  - en
ID  - AIHPB_2011__47_1_80_0
ER  - 
%0 Journal Article
%A Asselah, Amine
%T Annealed upper tails for the energy of a charged polymer
%J Annales de l'I.H.P. Probabilités et statistiques
%D 2011
%P 80-110
%V 47
%N 1
%I Gauthier-Villars
%U http://archive.numdam.org/articles/10.1214/09-AIHP355/
%R 10.1214/09-AIHP355
%G en
%F 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, Tome 47 (2011) no. 1, pp. 80-110. doi : 10.1214/09-AIHP355. http://archive.numdam.org/articles/10.1214/09-AIHP355/

[1] A. Asselah. Annealed lower tails for the energy of a charged polymer. J. Stat. Phys. To appear. | MR | Zbl

[2] A. Asselah. Shape transition under excess self-intersection for transient random walk. Ann. Henri Poincaré. To appear. | Numdam | MR | Zbl

[3] A. Asselah. Large deviations principle for self-intersection local times for simple random walk in dimension d > 4. ALEA 6 (2009) 281-322. | MR | Zbl

[4] A. Asselah. Large deviations for the self-intersection times for simple random walk in dimension 3. Probab. Theory Related Fields 141 (2008) 19-45. | MR | Zbl

[5] A. Asselah and F. Castell. Random walk in random scenery and self-intersection local times in dimensions d ≥ 5. Probab. Theory Related Fields 138 (2007) 1-32. | MR | Zbl

[6] A. Asselah and F. Castell. A note on random walk in random scenery. Ann. Inst. H. Poincaré Probab. Statist. 43 (2007) 163-173. | Numdam | MR | Zbl

[7] X. Chen. Random Walk Intersections: Large Deviations and Related Topics. Mathematical Surveys and Monographs 157. AMS, Providence, RI, 2009. | MR | Zbl

[8] X. Chen. Limit laws for the energy of a charged polymer. Ann. Inst. H. Poincaré Probab. Statist. 44 (2008) 638-672. | Numdam | MR | Zbl

[9] X. Chen and D. Khoshnevisan. From charged polymers to random walk in random scenery. In Proceedings of the Third Erich L. Lehmann Symposium. IMS Lecture Notes-Monograph Series 57 237-251, 2009. | MR

[10] B. Derrida, R. B. Griffith and P. G. Higgs. A model of directed walks with random interactions. Europhys. Lett. 18 (1992) 361-366.

[11] N. Gantert, R. Van Der Hofstad and W. König. Deviations of a random walk in a random scenery with stretched exponential tails. Stochastic Process. Appl. 116 (2006) 480-492. | MR | Zbl

[12] G. Giacomin. Random Polymer Models. Imperial College Press, London, 2007. | MR | Zbl

[13] R. Van Der Hofstad and W. König. A survey of one-dimensional random polymers. J. Statist. Phys. 103 (2001) 915-944. | MR | Zbl

[14] F. Den Hollander. Random Polymers. Lecture Notes in Mathematics 1974. Springer, Berlin, 2009. | MR | Zbl

[15] G. Lawler, M. Bramson and D. Griffeath. Internal diffusion limited aggregation. Ann. Probab. 20 (1992) 2117-2140. | MR | Zbl

[16] A. Nagaev. Integral limit theorems for large deviations when Cramer's condition is not fulfilled. Teor. Verojatnost. i Primenen. 14 (1969) 51-64, 203-216 (in Russian). | MR | Zbl

[17] S. Nagaev. Large deviations of sums of independent random variables. Ann. Probab. 7 (1979) 745-789. | MR | Zbl

Cité par Sources :