Convergence of the KMP model to the KPZ equation
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914001549524992 |
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| author | Barraquand, Guillaume Casini, Francesco |
| author_facet | Barraquand, Guillaume Casini, Francesco |
| contents | We prove that the Kipnis-Marchioro-Presutti (KMP) process converges to the Kardar-Parisi-Zhang (KPZ) equation, as time $t$ goes to infinity, in a properly scaled observation window shifted by $t^{3/4}$. Our proof is based on identifying the KMP process with a stochastic flow of kernels describing transition probabilities in a certain model of random walk in space-time random environment. This allows to apply a recent result of arXiv:2401.06073 proving convergence of the density field of random walks in random environment to the KPZ equation in a suitably general sense. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_19222 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Convergence of the KMP model to the KPZ equation Barraquand, Guillaume Casini, Francesco Probability Statistical Mechanics Mathematical Physics We prove that the Kipnis-Marchioro-Presutti (KMP) process converges to the Kardar-Parisi-Zhang (KPZ) equation, as time $t$ goes to infinity, in a properly scaled observation window shifted by $t^{3/4}$. Our proof is based on identifying the KMP process with a stochastic flow of kernels describing transition probabilities in a certain model of random walk in space-time random environment. This allows to apply a recent result of arXiv:2401.06073 proving convergence of the density field of random walks in random environment to the KPZ equation in a suitably general sense. |
| title | Convergence of the KMP model to the KPZ equation |
| topic | Probability Statistical Mechanics Mathematical Physics |
| url | https://arxiv.org/abs/2507.19222 |