Limit laws for the energy of a charged polymer

Xia Chen

Annales de l'I.H.P. Probabilités et statistiques (2008)

  • Volume: 44, Issue: 4, page 638-672
  • ISSN: 0246-0203

Abstract

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In this paper we obtain the central limit theorems, moderate deviations and the laws of the iterated logarithm for the energy Hn=∑1≤j<k≤nωjωk1{Sj=Sk} of the polymer {S1, …, Sn} equipped with random electrical charges {ω1, …, ωn}. Our approach is based on comparison of the moments between Hn and the self-intersection local time Qn=∑1≤j<k≤n1{Sj=Sk} run by the d-dimensional random walk {Sk}. As partially needed for our main objective and partially motivated by their independent interest, the central limit theorems and exponential integrability for Qn are also investigated in the case d≥3.

How to cite

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Chen, Xia. "Limit laws for the energy of a charged polymer." Annales de l'I.H.P. Probabilités et statistiques 44.4 (2008): 638-672. <http://eudml.org/doc/77986>.

@article{Chen2008,
abstract = {In this paper we obtain the central limit theorems, moderate deviations and the laws of the iterated logarithm for the energy Hn=∑1≤j&lt;k≤nωjωk1\{Sj=Sk\} of the polymer \{S1, …, Sn\} equipped with random electrical charges \{ω1, …, ωn\}. Our approach is based on comparison of the moments between Hn and the self-intersection local time Qn=∑1≤j&lt;k≤n1\{Sj=Sk\} run by the d-dimensional random walk \{Sk\}. As partially needed for our main objective and partially motivated by their independent interest, the central limit theorems and exponential integrability for Qn are also investigated in the case d≥3.},
author = {Chen, Xia},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {charged polymer; self-intersection local time; central limit theorem; moderate deviation; laws of the iterated logarithm},
language = {eng},
number = {4},
pages = {638-672},
publisher = {Gauthier-Villars},
title = {Limit laws for the energy of a charged polymer},
url = {http://eudml.org/doc/77986},
volume = {44},
year = {2008},
}

TY - JOUR
AU - Chen, Xia
TI - Limit laws for the energy of a charged polymer
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2008
PB - Gauthier-Villars
VL - 44
IS - 4
SP - 638
EP - 672
AB - In this paper we obtain the central limit theorems, moderate deviations and the laws of the iterated logarithm for the energy Hn=∑1≤j&lt;k≤nωjωk1{Sj=Sk} of the polymer {S1, …, Sn} equipped with random electrical charges {ω1, …, ωn}. Our approach is based on comparison of the moments between Hn and the self-intersection local time Qn=∑1≤j&lt;k≤n1{Sj=Sk} run by the d-dimensional random walk {Sk}. As partially needed for our main objective and partially motivated by their independent interest, the central limit theorems and exponential integrability for Qn are also investigated in the case d≥3.
LA - eng
KW - charged polymer; self-intersection local time; central limit theorem; moderate deviation; laws of the iterated logarithm
UR - http://eudml.org/doc/77986
ER -

References

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