Scaling limits for random walks on long range percolation clusters
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911893531131904 |
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| author | Berger, Noam Tokushige, Yuki |
| author_facet | Berger, Noam Tokushige, Yuki |
| contents | We study limit laws for simple random walks on supercritical long-range percolation clusters on the integer lattice. For the long range percolation model, the probability that two vertices are connected behaves asymptotically as a negative power of distance between them. We prove that the scaling limit of simple random walk on the infinite component converges to an isotropic alpha-stable Levy process. This complements the work of Crawford and Sly, who proved the corresponding result for alpha between 0 and 1. The convergence holds in both the quenched and annealed senses. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_18532 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Scaling limits for random walks on long range percolation clusters Berger, Noam Tokushige, Yuki Probability 60K37, 35B27 We study limit laws for simple random walks on supercritical long-range percolation clusters on the integer lattice. For the long range percolation model, the probability that two vertices are connected behaves asymptotically as a negative power of distance between them. We prove that the scaling limit of simple random walk on the infinite component converges to an isotropic alpha-stable Levy process. This complements the work of Crawford and Sly, who proved the corresponding result for alpha between 0 and 1. The convergence holds in both the quenched and annealed senses. |
| title | Scaling limits for random walks on long range percolation clusters |
| topic | Probability 60K37, 35B27 |
| url | https://arxiv.org/abs/2403.18532 |