Logarithmic fluctuations of Stationary Hastings-Levitov
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909479808794624 |
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| author | Berger, Noam Procaccia, Eviatar B. |
| author_facet | Berger, Noam Procaccia, Eviatar B. |
| contents | We prove that the fluctuation field $\{M_t(x)\}_{x\in\mathbb{R}}$ of stationary Hastings-Levitov$(0)$ exhibits logarithmic spatial correlations. Moreover, by studying the infinitesimal generator of the imaginary part of $M_t(0)$, we show that for some $β>0$, $\max_{x\in[0,t]}\text{Im} M_t(x)<β\log t$ with high probability, as $t\to\infty$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_03554 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Logarithmic fluctuations of Stationary Hastings-Levitov Berger, Noam Procaccia, Eviatar B. Probability Mathematical Physics We prove that the fluctuation field $\{M_t(x)\}_{x\in\mathbb{R}}$ of stationary Hastings-Levitov$(0)$ exhibits logarithmic spatial correlations. Moreover, by studying the infinitesimal generator of the imaginary part of $M_t(0)$, we show that for some $β>0$, $\max_{x\in[0,t]}\text{Im} M_t(x)<β\log t$ with high probability, as $t\to\infty$. |
| title | Logarithmic fluctuations of Stationary Hastings-Levitov |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2502.03554 |