Mesoscopic averaging of the two-dimensional KPZ equation
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866916075739807744 |
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| author | Tao, Ran |
| author_facet | Tao, Ran |
| contents | We study the limit of a local average of the KPZ equation in dimension $d=2$ with general initial data in the subcritical regime. Our result shows that a proper spatial averaging of the KPZ equation converges in distribution to the sum of the solution to a deterministic KPZ equation and a Gaussian random variable that depends solely on the scale of averaging. This shows a unique mesoscopic averaging phenomenon that is only present in dimension two. Our work is inspired by the recent findings by Chatterjee \cite{chatterjee2021weak}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_06689 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Mesoscopic averaging of the two-dimensional KPZ equation Tao, Ran Probability Mathematical Physics We study the limit of a local average of the KPZ equation in dimension $d=2$ with general initial data in the subcritical regime. Our result shows that a proper spatial averaging of the KPZ equation converges in distribution to the sum of the solution to a deterministic KPZ equation and a Gaussian random variable that depends solely on the scale of averaging. This shows a unique mesoscopic averaging phenomenon that is only present in dimension two. Our work is inspired by the recent findings by Chatterjee \cite{chatterjee2021weak}. |
| title | Mesoscopic averaging of the two-dimensional KPZ equation |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2302.06689 |