带周期电荷高分子链的无限体积极限
Infinite volume limits of polymer chains with periodic charges
摘要：
本文的目的是双重的：-给一个明确的公式的自由能的一般类的聚合物链通过周期性的潜力与环境相互作用的一个基本的和自足的证明。这推广了[Bolthausen and Giacomin，AAP 2005]中的一个结果，其中公式是通过使用马尔可夫链的Donsker-Varadhan大偏差理论推导出来的。相反，我们利用更新理论的工具。- 确定系统的无限容量极限。特别是，在不同的状态中，我们会遇到瞬时、零循环和正循环过程（对应于轨迹的离域、临界和局部行为）。这是通过利用更新理论方法获得的系统的分拆函数的尖锐估计。系统无限体积极限的精确表征暴露了一个非唯一性问题。然而，我们将详细解释这种（最初）令人惊讶的现象是如何由于一阶相变的存在而引起的。
英文摘要：
The aim of this paper is twofold: - To give an elementary and self-contained proof of an explicit formula for the free energy for a general class of polymer chains interacting with an environment through periodic potentials. This generalizes a result in [Bolthausen and Giacomin, AAP 2005] in which the formula is derived by using the Donsker-Varadhan Large Deviations theory for Markov chains. We exploit instead tools from renewal theory. - To identify the infinite volume limits of the system. In particular, in the different regimes we encounter transient, null recurrent and positive recurrent processes (which correspond to delocalized, critical and localized behaviors of the trajectories). This is done by exploiting the sharp estimates on the partition function of the system obtained by the renewal theory approach. The precise characterization of the infinite volume limits of the system exposes a non-uniqueness problem. We will however explain in detail how this (at first) surprising phenomenon is instead due to the presence of a first-order phase transition.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
