Sharp asymptotics of disconnection time of large cylinders by simple and biased random walks
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909327193800704 |
|---|---|
| author | Li, Xinyi Liu, Yu Wang, Yuanzheng |
| author_facet | Li, Xinyi Liu, Yu Wang, Yuanzheng |
| contents | We investigate the asymptotic disconnection time of a large discrete cylinder $(\mathbb{Z}/N\mathbb{Z})^{d}\times \mathbb{Z}$, $d\geq 2$, by simple and biased random walks. For simple random walk, we derive a sharp asymptotic lower bound that matches the upper bound from [Sznitman, Ann. Probab., 2009]. For biased walks, we obtain bounds that asymptotically match in the principal order when the bias is not too strong, which greatly improves non-matching bounds from [Windisch, Ann. Appl. Probab., 2008]. As a crucial tool in the proof, we also obtain a "very strong" coupling between the trace of random walk on the cylinder and random interlacements, which is of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_17900 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sharp asymptotics of disconnection time of large cylinders by simple and biased random walks Li, Xinyi Liu, Yu Wang, Yuanzheng Probability 60G50, 60K35, 82C41 (Primary) We investigate the asymptotic disconnection time of a large discrete cylinder $(\mathbb{Z}/N\mathbb{Z})^{d}\times \mathbb{Z}$, $d\geq 2$, by simple and biased random walks. For simple random walk, we derive a sharp asymptotic lower bound that matches the upper bound from [Sznitman, Ann. Probab., 2009]. For biased walks, we obtain bounds that asymptotically match in the principal order when the bias is not too strong, which greatly improves non-matching bounds from [Windisch, Ann. Appl. Probab., 2008]. As a crucial tool in the proof, we also obtain a "very strong" coupling between the trace of random walk on the cylinder and random interlacements, which is of independent interest. |
| title | Sharp asymptotics of disconnection time of large cylinders by simple and biased random walks |
| topic | Probability 60G50, 60K35, 82C41 (Primary) |
| url | https://arxiv.org/abs/2409.17900 |