Subcritical limits of a 1D KPZ growth surface with finite moments
Dang-Zheng Liu, Fangzhou Luo, Tian Wu, Yuxuan Zong
Source abstract
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.
Evidence graph
No public relationships recorded yet.
Integrity note: This page is a factual metadata record created by deterministic ingestion. It is not a claim that the work moves a mathematical frontier or has been independently verified.