标题： 离散运动聚合物的有效半径 显示英文标题

标题： Effective Radius of a Discrete Moving Polymer

摘要： 我们提出一个离散时空随机偏微分方程（SPDE）模型来描述具有固有长度$J$的弱自避聚合物的动力学。通过引入针对离散设置量身定制的惩罚因子，我们证明了聚合物的均方根半径与$J$成线性比例。这种标度行为不同于 Mueller 和 Neuman\cite{mueller2022scaling}在连续框架中推导出的定律，突显了离散模型的独特性质及其在研究晶格状环境中聚合物行为时的分析可处理性。 显示英文摘要

摘要： We present a discrete space-time stochastic partial differential equation (SPDE) model to describe the dynamics of a weakly self-avoiding polymer with intrinsic length $J$. By introducing a penalty factor tailored to the discrete setting, we establish that the polymer's root mean squared radius scales linearly with $J$. This scaling behavior differs from the law derived by Mueller and Neuman \cite{mueller2022scaling} in the continuous framework, highlighting both the distinct nature of the discrete model and its analytical tractability for studying polymer behavior in lattice-like environments.