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.

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: 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
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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/articles/10.1214/07-AIHP120/

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