Fluctuation exponents of the open KPZ equation in the maximal current phase
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| Format: | Preprint |
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2025
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| _version_ | 1866909737443917824 |
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| author | Hip, Andres A. Contreras Das, Sayan Zitridis, Antonios |
| author_facet | Hip, Andres A. Contreras Das, Sayan Zitridis, Antonios |
| contents | We consider the open KPZ equation $H(x,t)$ on the interval $[0,L]$ with Neumann boundary conditions depending on parameters $u,v\ge 0$ (the so-called maximal current phase). For $L \sim t^α$ and stationary initial conditions, we obtain matching upper and lower bounds on the variance of the height function $H(0,t)$ for $α\in [0,\frac23]$. Our proof combines techniques from arXiv:2111.03650, which treated the periodic KPZ equation, with Gibbsian line ensemble methods based on the probabilistic structure of the stationary measures developed in arXiv:2103.12253, arXiv:2105.15178, arXiv:2105.03946, arXiv:2306.05983, arXiv:2404.13444. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_11094 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fluctuation exponents of the open KPZ equation in the maximal current phase Hip, Andres A. Contreras Das, Sayan Zitridis, Antonios Probability Mathematical Physics We consider the open KPZ equation $H(x,t)$ on the interval $[0,L]$ with Neumann boundary conditions depending on parameters $u,v\ge 0$ (the so-called maximal current phase). For $L \sim t^α$ and stationary initial conditions, we obtain matching upper and lower bounds on the variance of the height function $H(0,t)$ for $α\in [0,\frac23]$. Our proof combines techniques from arXiv:2111.03650, which treated the periodic KPZ equation, with Gibbsian line ensemble methods based on the probabilistic structure of the stationary measures developed in arXiv:2103.12253, arXiv:2105.15178, arXiv:2105.03946, arXiv:2306.05983, arXiv:2404.13444. |
| title | Fluctuation exponents of the open KPZ equation in the maximal current phase |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2508.11094 |