Solidification estimates for random walks on supercritical percolation clusters
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915812719198208 |
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| author | Chiarini, Alberto Liu, Zhizhou Nitzschner, Maximilian |
| author_facet | Chiarini, Alberto Liu, Zhizhou Nitzschner, Maximilian |
| contents | We consider the simple random walk on the infinite cluster of a general class of percolation models on $\mathbb{Z}^d$, $d\geq 3$, including Bernoulli percolation as well as models with strong, algebraically decaying correlations. For almost every realization of the percolation configuration, we obtain uniform controls on the absorption probability of a random walk by certain "porous interfaces" surrounding the discrete blow-up of a compact set $A$. These controls substantially generalize previous results obtained in arXiv:1706.07229 for Brownian motion in $\mathbb{R}^d$ and in arXiv:2012.05230 for random walks on $\mathbb{Z}^d$ equipped with uniformly elliptic edge weights to a manifestly non-elliptic framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_19929 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Solidification estimates for random walks on supercritical percolation clusters Chiarini, Alberto Liu, Zhizhou Nitzschner, Maximilian Probability 60J45, 60K37, 60K35, 82B43 We consider the simple random walk on the infinite cluster of a general class of percolation models on $\mathbb{Z}^d$, $d\geq 3$, including Bernoulli percolation as well as models with strong, algebraically decaying correlations. For almost every realization of the percolation configuration, we obtain uniform controls on the absorption probability of a random walk by certain "porous interfaces" surrounding the discrete blow-up of a compact set $A$. These controls substantially generalize previous results obtained in arXiv:1706.07229 for Brownian motion in $\mathbb{R}^d$ and in arXiv:2012.05230 for random walks on $\mathbb{Z}^d$ equipped with uniformly elliptic edge weights to a manifestly non-elliptic framework. |
| title | Solidification estimates for random walks on supercritical percolation clusters |
| topic | Probability 60J45, 60K37, 60K35, 82B43 |
| url | https://arxiv.org/abs/2508.19929 |