Lipschitz-continuity of time constant in generalized First-passage percolation
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866917691952988160 |
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| author | Can, Van Hao Nakajima, Shuta Nguyen, Van Quyet |
| author_facet | Can, Van Hao Nakajima, Shuta Nguyen, Van Quyet |
| contents | In this article, we consider a generalized First-passage percolation model, where each edge in $\mathbb{Z}^d$ is independently assigned an infinite weight with probability $1-p$, and a random finite weight otherwise. The existence and positivity of the time constant have been established in [CT16]. Recently, using sophisticated multi-scale renormalizations, Cerf and Dembin [CD22] proved that the time constant of chemical distance in super-critical percolation is Lipschitz continuous. In this work, we propose a different approach leveraging lattice animal theory and a simple one-step renormalization with the aid of Russo's formula, to show the Lipschitz continuity of the time constant in generalized First-passage percolation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_03550 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Lipschitz-continuity of time constant in generalized First-passage percolation Can, Van Hao Nakajima, Shuta Nguyen, Van Quyet Probability In this article, we consider a generalized First-passage percolation model, where each edge in $\mathbb{Z}^d$ is independently assigned an infinite weight with probability $1-p$, and a random finite weight otherwise. The existence and positivity of the time constant have been established in [CT16]. Recently, using sophisticated multi-scale renormalizations, Cerf and Dembin [CD22] proved that the time constant of chemical distance in super-critical percolation is Lipschitz continuous. In this work, we propose a different approach leveraging lattice animal theory and a simple one-step renormalization with the aid of Russo's formula, to show the Lipschitz continuity of the time constant in generalized First-passage percolation. |
| title | Lipschitz-continuity of time constant in generalized First-passage percolation |
| topic | Probability |
| url | https://arxiv.org/abs/2312.03550 |