Environment viewed from the particle and slowdown for ballistic RWRE in low dimensions
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866916876093751296 |
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| author | Peretz, Tal |
| author_facet | Peretz, Tal |
| contents | We consider a random walk in a random environment on $\mathbb{Z}^d$ under ballisticity condition $(T)$. We show the existence of the invariant measure $Q$ with respect to the environment viewed from the particle for $d=2$ and $d=3$, which disproves a conjecture made in arXiv:1405.6819 regarding the two-dimensional case. We also prove tail estimates for the Radon-Nikodym derivative $dQ/dP$, where $P$ is the original distribution on the environment. Lastly, we provide nearly sharp tail bounds for regeneration times for $d=3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_12238 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Environment viewed from the particle and slowdown for ballistic RWRE in low dimensions Peretz, Tal Probability 60K37, 82D30 We consider a random walk in a random environment on $\mathbb{Z}^d$ under ballisticity condition $(T)$. We show the existence of the invariant measure $Q$ with respect to the environment viewed from the particle for $d=2$ and $d=3$, which disproves a conjecture made in arXiv:1405.6819 regarding the two-dimensional case. We also prove tail estimates for the Radon-Nikodym derivative $dQ/dP$, where $P$ is the original distribution on the environment. Lastly, we provide nearly sharp tail bounds for regeneration times for $d=3$. |
| title | Environment viewed from the particle and slowdown for ballistic RWRE in low dimensions |
| topic | Probability 60K37, 82D30 |
| url | https://arxiv.org/abs/2204.12238 |