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 = 1j<kn ω j ω k 1 S j =S k of the polymer S 1 ,...,S n equipped with random electrical charges ω 1 ,...,ω n . Our approach is based on comparison of the moments between H n and the self-intersection local time Q n = 1j<kn 1 S j =S k run by the d-dimensional random walk S k . 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 d3.

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 = 1j<kn ω j ω k 1 S j =S k du polymère S 1 ,...,S n doté de charges électriques ω 1 ,...,ω n . Notre approche se base sur la comparaison des moments de H n et du temps local de recoupements Q n = 1j<kn 1 S j =S k de la marche aléatoire d-dimensionnelle S k . L’étude du théorème central limite et de l’intégrabilité exponentielle de Q n (dans le cas d3) 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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