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Spatial decorrelation of KPZ from narrow wedge
Yu Gu, Fei Pu · 2025-06-29 · via math.PR updates on arXiv.org

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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