Work

A functional central limit theorem for the KPZ equation with narrow wedge initial data

Year: 2026

Type: preprint

Abstract: In this article, we consider the Kardar-Parisi-Zhang (KPZ) equation with narrow wedge initial data. We prove a functional central limit theorem for the spatial average of the solution, which solves an open problem from Gu and Pu (2025). Our main tool is Clark-Ocone formula from Malliavin calculus, combined with an in-depth analysis of the increments of the solution. The main step is a moment bound for time increments of the normalized spatial integral. For this, we introduce a new technique, called a ``common-ray'' change of variables. Using the fact that Malliavin derivative of the solution satisfies a Chapman-Kolmogorov relation, we reduce the kernel differences at two times to spatial increments at one common time.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.27219

Authors: Balan, Raluca M., Chen, Le, Wang, Jinxin

Institutions: University of Ottawa, Auburn University

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Auburn University, Mitacs, Natural Sciences and Engineering Research Council of Canada

Award: CAREER: Stochastic Partial Differential Equations: Analysis and Applications

OpenAlex ID: W7223147551

Cites: 3

Cited by:

Related to: 10