High Temperature Behaviors of the Directed Polymer on a Cylinder
High Temperature Behaviors of the Directed Polymer on a Cylinder
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DOI：
10.1007/s10955-022-02899-2
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发表时间：
2022-02
影响因子：
1.6
通讯作者：
Yu Gu;T. Komorowski
中科院分区：
文献类型：
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作者：
Yu Gu;T. Komorowski
本文研究了半径为L的圆柱体上定向聚合物的自由能。假设随机环境是由一个高斯过程，这是白色在时间和空间上光滑，与任意的compounds支持的空间协方差函数，我们得到精确的标度行为的极限自由能为高温，其次是大，在所有维度。我们的方法是基于一个微扰扩展的PDE层次满足的聚合物端点分布的多点相关函数。对于空时白色噪声随机环境，我们导出了极限自由能的显式表达式。
In this paper, we study the free energy of the directed polymer on a cylinder of radiusLwith the inverse temperature. Assuming the random environment is given by a Gaussian process that is white in time and smooth in space, with an arbitrary compactly supported spatial covariance function, we obtain precise scaling behaviors of the limiting free energy for high temperatures, followed by large, in all dimensions. Our approach is based on a perturbative expansion of the PDE hierarchy satisfied by the multipoint correlation function of the polymer endpoint distribution. For the random environment given by thespacetime white noise, we derive an explicit expression of the limiting free energy.