The scaling limit of critical hypercube percolation
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910310457147392 |
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| author | Blanc-Renaudie, Arthur Broutin, Nicolas Nachmias, Asaf |
| author_facet | Blanc-Renaudie, Arthur Broutin, Nicolas Nachmias, Asaf |
| contents | We study the connected components in critical percolation on the Hamming hypercube $\{0,1\}^m$. We show that their sizes rescaled by $2^{-2m/3}$ converge in distribution, and that, considered as metric measure spaces with the graph distance rescaled by $2^{-m/3}$ and the uniform measure, they converge in distribution with respect to the Gromov-Hausdorff-Prokhorov topology. The two corresponding limits are as in critical Erdős-Rényi graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_16365 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The scaling limit of critical hypercube percolation Blanc-Renaudie, Arthur Broutin, Nicolas Nachmias, Asaf Probability 60D05, 60F05, 60K35 We study the connected components in critical percolation on the Hamming hypercube $\{0,1\}^m$. We show that their sizes rescaled by $2^{-2m/3}$ converge in distribution, and that, considered as metric measure spaces with the graph distance rescaled by $2^{-m/3}$ and the uniform measure, they converge in distribution with respect to the Gromov-Hausdorff-Prokhorov topology. The two corresponding limits are as in critical Erdős-Rényi graphs. |
| title | The scaling limit of critical hypercube percolation |
| topic | Probability 60D05, 60F05, 60K35 |
| url | https://arxiv.org/abs/2401.16365 |