Spatial decorrelation of KPZ from narrow wedge
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908427585847296 |
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| author | Gu, Yu Pu, Fei |
| author_facet | Gu, Yu Pu, Fei |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_23065 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spatial decorrelation of KPZ from narrow wedge Gu, Yu Pu, Fei Probability 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. |
| title | Spatial decorrelation of KPZ from narrow wedge |
| topic | Probability |
| url | https://arxiv.org/abs/2506.23065 |