Weak coupling limit of KPZ with rougher than white noise
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908330337763328 |
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| author | Gerencsér, Máté Toninelli, Fabio |
| author_facet | Gerencsér, Máté Toninelli, Fabio |
| contents | We consider the KPZ equation in $1$ spatial dimension with noise that is rougher than white by an exponent $γ>1/4$. Under a weak coupling limit, formally removing the nonlinearity from the equation, we show using regularity structures that the renormalised solutions converge to a Gaussian limit that is different from the solution of the linear part of the equation. The regime of this effect has a nontrivial overlap with the subcritical regime $γ<1/2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_08364 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weak coupling limit of KPZ with rougher than white noise Gerencsér, Máté Toninelli, Fabio Probability Analysis of PDEs We consider the KPZ equation in $1$ spatial dimension with noise that is rougher than white by an exponent $γ>1/4$. Under a weak coupling limit, formally removing the nonlinearity from the equation, we show using regularity structures that the renormalised solutions converge to a Gaussian limit that is different from the solution of the linear part of the equation. The regime of this effect has a nontrivial overlap with the subcritical regime $γ<1/2$. |
| title | Weak coupling limit of KPZ with rougher than white noise |
| topic | Probability Analysis of PDEs |
| url | https://arxiv.org/abs/2406.08364 |