Quenched scaling limit for biased random walks on random, heavy tailed conductances: low dimensions
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912500082016256 |
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| author | De Ambroggio, Umberto Scali, Carlo |
| author_facet | De Ambroggio, Umberto Scali, Carlo |
| contents | We consider a random walk amongst positive random conductances on $\mathbb{Z}^d, d \ge 2$, with directional bias. When the conductances have a stable distribution with parameter $γ\in (0, 1)$, the walk is sub-ballistic. In this regime Fribergh and Kious (Ann. Prob. 2018) derived an annealed scaling limit for the appropriately rescaled walk towards the Fractional Kinetics process. We prove the quenched version of this result for all $d \ge 2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_17583 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quenched scaling limit for biased random walks on random, heavy tailed conductances: low dimensions De Ambroggio, Umberto Scali, Carlo Probability 60K37, 60F17 We consider a random walk amongst positive random conductances on $\mathbb{Z}^d, d \ge 2$, with directional bias. When the conductances have a stable distribution with parameter $γ\in (0, 1)$, the walk is sub-ballistic. In this regime Fribergh and Kious (Ann. Prob. 2018) derived an annealed scaling limit for the appropriately rescaled walk towards the Fractional Kinetics process. We prove the quenched version of this result for all $d \ge 2$. |
| title | Quenched scaling limit for biased random walks on random, heavy tailed conductances: low dimensions |
| topic | Probability 60K37, 60F17 |
| url | https://arxiv.org/abs/2507.17583 |