One-arm domination time in Cylindrical Hastings-Levitov$(0)$
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908450371403776 |
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| author | Chen, Guanyi Procaccia, Eviatar B. Zong, Yuxuan |
| author_facet | Chen, Guanyi Procaccia, Eviatar B. Zong, Yuxuan |
| contents | The cylindrical Hastings-Levitov$(0)$ admits a single infinite connected tree (arm). For a cylinder of width $N$, and particles of size $λ$, we consider the last time $\upsilon_{N, λ}$, that a finite tree receives a particle. We prove that $\frac{cN^2}{λ^3}<\mathbb{E}[\upsilon_{N, λ}]< \frac{CN^2}{λ^3}$. Furthermore, we establish an exponential tail for $\upsilon_{N, λ}$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_11028 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | One-arm domination time in Cylindrical Hastings-Levitov$(0)$ Chen, Guanyi Procaccia, Eviatar B. Zong, Yuxuan Probability Mathematical Physics The cylindrical Hastings-Levitov$(0)$ admits a single infinite connected tree (arm). For a cylinder of width $N$, and particles of size $λ$, we consider the last time $\upsilon_{N, λ}$, that a finite tree receives a particle. We prove that $\frac{cN^2}{λ^3}<\mathbb{E}[\upsilon_{N, λ}]< \frac{CN^2}{λ^3}$. Furthermore, we establish an exponential tail for $\upsilon_{N, λ}$. |
| title | One-arm domination time in Cylindrical Hastings-Levitov$(0)$ |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2507.11028 |