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Subcritical limits of a 1D KPZ growth surface with finite moments

  • Dang-Zheng Liu
  • Fangzhou Luo
  • Tian Wu
  • Yuxuan Zong
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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.

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Cite

BibTeXRIS
BibTeX
@misc{liu2026subcritical,
  title = {{Subcritical limits of a 1D KPZ growth surface with finite moments}},
  author = {Dang-Zheng Liu and Fangzhou Luo and Tian Wu and Yuxuan Zong},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.08308},
  eprint = {2609.08308},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.08308},
}
RIS
TY  - UNPB
TI  - Subcritical limits of a 1D KPZ growth surface with finite moments
AU  - Dang-Zheng Liu
AU  - Fangzhou Luo
AU  - Tian Wu
AU  - Yuxuan Zong
PY  - 2026
DA  - 2026/09/08
PB  - arXiv
DO  - 10.48550/arxiv.2609.08308
UR  - https://arxiv.org/abs/2609.08308
AB  - 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.
ER  -