Biased random walk on dynamical percolation
Fuente:
arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866916409976553472 |
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| author | Andres, Sebastian Gantert, Nina Schmid, Dominik Sousi, Perla |
| author_facet | Andres, Sebastian Gantert, Nina Schmid, Dominik Sousi, Perla |
| contents | We study biased random walks on dynamical percolation on $\mathbb{Z}^d$. We establish a law of large numbers and an invariance principle for the random walk using regeneration times. Moreover, we verify that the Einstein relation holds, and we investigate the speed of the walk as a function of the bias. While for $d=1$ the speed is increasing, we show that in general this fails in dimension $d \geq 2$. As our main result, we establish two regimes of parameters, separated by an explicit critical curve, such that the speed is either eventually strictly increasing or eventually strictly decreasing. This is in sharp contrast to the biased random walk on a static supercritical percolation cluster, where the speed is known to be eventually zero. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_05208 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Biased random walk on dynamical percolation Andres, Sebastian Gantert, Nina Schmid, Dominik Sousi, Perla Probability 60K35, 60K37 We study biased random walks on dynamical percolation on $\mathbb{Z}^d$. We establish a law of large numbers and an invariance principle for the random walk using regeneration times. Moreover, we verify that the Einstein relation holds, and we investigate the speed of the walk as a function of the bias. While for $d=1$ the speed is increasing, we show that in general this fails in dimension $d \geq 2$. As our main result, we establish two regimes of parameters, separated by an explicit critical curve, such that the speed is either eventually strictly increasing or eventually strictly decreasing. This is in sharp contrast to the biased random walk on a static supercritical percolation cluster, where the speed is known to be eventually zero. |
| title | Biased random walk on dynamical percolation |
| topic | Probability 60K35, 60K37 |
| url | https://arxiv.org/abs/2301.05208 |