Limit laws for the energy of a charged polymer
Limit laws for the energy of a charged polymer
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DOI：
10.1214/07-aihp120
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发表时间：
2008-08
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影响因子：
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通讯作者：
Xia Chen
中科院分区：
文献类型：
--
作者：
Xia Chen
本文得到了具有随机电荷的聚合物S_1，…，S_n的能量[H_n=\sum_{1\le j<；k\le n}\omega_j\omega_k1{{S_j=S_k}}]的中心极限定理、中偏差和重对数律。我们的方法是基于$d$维随机游动的自交局部时间[Q_n=\sum_{1\le j<；k\le n}1_{{S_j=S_k}}]与$H_n之间的矩的比较。作为我们的主要目标的一部分需要和他们的独立利益的部分动机，在$d3$的情况下也研究了$q_n$的中心极限定理和指数可积性。
In this paper we obtain the central limit theorems, moderate deviations and the laws of the iterated logarithm for the energy \[H_n=\sum_{1\le j<k\le n}\omega_j\omega_k1_{\{S_j=S_k\}}\] of the polymer $\{S_1,...,S_n\}$ equipped with random electrical charges $\{\omega_1,...,\omega_n\}$. Our approach is based on comparison of the moments between $H_n$ and the self-intersection local time \[Q_n=\sum_{1\le j<k\le n}1_{\{S_j=S_k\}}\] 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 $d\ge3$.