Spatial decorrelation of KPZ from narrow wedge

Yu Gu; Fei Pu

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arXiv · 2506.23065

Spatial decorrelation of KPZ from narrow wedge

Yu Gu·Fei Pu

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Abstract

We study the spatial decorrelation of the solution to the KPZ equation with narrow wedge initial data. For fixed $t>0$, we determine the decay rate of the spatial covariance function, showing that ${\rm Cov}[h(t,x),h(t,0)]\sim \frac{t}{x}$ as $x\to\infty$. In addition, we prove that the finite-dimensional distributions of the properly rescaled spatial average of the height function converge to those of a Brownian motion.

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Yu Gu, Fei Pu. 2025-06-29. Spatial decorrelation of KPZ from narrow wedge. https://arxiv.org/abs/2506.23065

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