发表机构
University of Science and Technology of China; Peking University（中国科学技术大学; 北京大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究一维随机增长曲面在亚临界条件下的极限行为，通过递归重整化方案和图的表示，证明了重缩放高度函数依分布收敛于加性随机热方程的解。
AI 中文摘要
我们考虑由Adhikari和Chatterjee [AC24]引入的一维随机增长曲面，其中高度函数通过两个相邻站点的高度和每个时空点上的独立噪声项递归定义。在亚临界状态下，假设噪声变量具有一致有界的八阶矩且驱动函数具有适当的正则性，我们建立了适当重缩放的高度函数依分布收敛于加性随机热方程的解。我们的方法采用直接递归重整化方案。一个核心组成部分是重整化项的图表示，这使得推导重整化过程所需的高阶矩界成为可能。
英文摘要
We consider the one-dimensional random growth surface introduced by Adhikari and Chatterjee [AC24], where the height function is defined recursively via the heights at two neighboring sites and an independent noise term at each space-time point. In the subcritical regime, assuming uniformly bounded eighth moments of the noise variables and appropriate regularity of the driving function, we establish convergence in law of the suitably rescaled height function to the solution of the additive stochastic heat equation. Our approach employs a direct recursive renormalization scheme. A central component is a graph representation of the renormalization terms, which enables the derivation of the high-moment bounds essential to the renormalization procedure.
Comments46 pages, 12 figures
