Limit laws for the energy of a charged polymer
Annales de l'I.H.P. Probabilités et statistiques, Volume 44 (2008) no. 4, p. 638-672

In this paper we obtain the central limit theorems, moderate deviations and the laws of the iterated logarithm for the energy ${H}_{n}=\sum _{1\le j of the polymer $\left\{{S}_{1},...,{S}_{n}\right\}$ equipped with random electrical charges $\left\{{\omega }_{1},...,{\omega }_{n}\right\}$. Our approach is based on comparison of the moments between ${H}_{n}$ and the self-intersection local time ${Q}_{n}=\sum _{1\le j run by the $d$-dimensional random walk $\left\{{S}_{k}\right\}$. As partially needed for our main objective and partially motivated by their independent interest, the central limit theorems and exponential integrability for ${Q}_{n}$ are also investigated in the case $d\ge 3$.

Cet article est consacré à l’étude du théorème central limite, des déviations modérées et des lois du logarithme itéré pour l’énergie ${H}_{n}=\sum _{1\le j du polymère $\left\{{S}_{1},...,{S}_{n}\right\}$ doté de charges électriques $\left\{{\omega }_{1},...,{\omega }_{n}\right\}$. Notre approche se base sur la comparaison des moments de ${H}_{n}$ et du temps local de recoupements ${Q}_{n}=\sum _{1\le j de la marche aléatoire $d$-dimensionnelle $\left\{{S}_{k}\right\}$. L’étude du théorème central limite et de l’intégrabilité exponentielle de ${Q}_{n}$ (dans le cas $d\ge 3$) est également menée, tant pour comme outil pour notre principal objectif que pour son intérêt intrinsèque.

DOI : https://doi.org/10.1214/07-AIHP120
Classification:  60F05,  60F10,  60F15
Keywords: charged polymer, self-intersection local time, central limit theorem, moderate deviation, laws of the iterated logarithm
@article{AIHPB_2008__44_4_638_0,
author = {Chen, Xia},
title = {Limit laws for the energy of a charged polymer},
journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
publisher = {Gauthier-Villars},
volume = {44},
number = {4},
year = {2008},
pages = {638-672},
doi = {10.1214/07-AIHP120},
zbl = {1178.60024},
mrnumber = {2446292},
language = {en},
url = {http://www.numdam.org/item/AIHPB_2008__44_4_638_0}
}

Chen, Xia. Limit laws for the energy of a charged polymer. Annales de l'I.H.P. Probabilités et statistiques, Volume 44 (2008) no. 4, pp. 638-672. doi : 10.1214/07-AIHP120. http://www.numdam.org/item/AIHPB_2008__44_4_638_0/

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