Biased random walk on the critical curve of dynamical percolation
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910822968590336 |
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| author | Olzhabayev, Assylbek Schmid, Dominik |
| author_facet | Olzhabayev, Assylbek Schmid, Dominik |
| contents | We study biased random walks on dynamical percolation in $\mathbb{Z}^d$, which were recently introduced by Andres et al. We provide a second order expansion for the asymptotic speed and show for $d \ge 2$ that the speed of the biased random walk on the critical curve is eventually monotone increasing. Our methods are based on studying the environment seen from the walker as well as a combination of ergodicity and several couplings arguments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_08568 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Biased random walk on the critical curve of dynamical percolation Olzhabayev, Assylbek Schmid, Dominik Probability 60K35, 60K37 We study biased random walks on dynamical percolation in $\mathbb{Z}^d$, which were recently introduced by Andres et al. We provide a second order expansion for the asymptotic speed and show for $d \ge 2$ that the speed of the biased random walk on the critical curve is eventually monotone increasing. Our methods are based on studying the environment seen from the walker as well as a combination of ergodicity and several couplings arguments. |
| title | Biased random walk on the critical curve of dynamical percolation |
| topic | Probability 60K35, 60K37 |
| url | https://arxiv.org/abs/2502.08568 |