论文标题
可集成的定向聚合物模型的浓度
Concentration for integrable directed polymer models
论文作者
论文摘要
在本文中，我们考虑了四个可集成的定向聚合物模型，已知自由能可以表现出KPZ波动。我们最近在O'Connell-Yor聚合物的工作中引入了对这些模型进行分析的共同框架。 我们使用迭代方法来得出分区函数（任何顺序）$ n^{1/3+ε} $的任何顺序的中心矩的估计。在利用不变结构的创新中，我们开发了用于自由能的功能与边界权重之间相关性的公式，这些函数通过出现在O'Connell-yor情况的分析中的零件中代替高斯集成的边界权重。
In this paper, we consider four integrable models of directed polymers for which the free energy is known to exhibit KPZ fluctuations. A common framework for the analysis of these models was introduced in our recent work on the O'Connell-Yor polymer. We derive estimates for the central moments of the partition function, of any order, on the near-optimal scale $N^{1/3+ε}$, using an iterative method. Among the innovations exploiting the invariant structure, we develop formulas for correlations between functions of the free energy and the boundary weights that replace the Gaussian integration by parts appearing in the analysis of the O'Connell-Yor case.
