A phase transition in Erdős-Barak random graphs
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909992418803712 |
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| author | Blanchard, Gilles Curien, Nicolas Krause, Klara Reisach, Alexander |
| author_facet | Blanchard, Gilles Curien, Nicolas Krause, Klara Reisach, Alexander |
| contents | We study monotone paths in Erdős-Rényi random graphs on numbered vertices. Benjamini & Tzalik established a phase transition at $p = \frac{\log n}{n}$ for this model. We refine the critical value to $p = \frac{\log n - \log \log n }{n}$ and identify the critical window of order $Θ(1/n)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_05756 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A phase transition in Erdős-Barak random graphs Blanchard, Gilles Curien, Nicolas Krause, Klara Reisach, Alexander Probability Combinatorics Statistics Theory We study monotone paths in Erdős-Rényi random graphs on numbered vertices. Benjamini & Tzalik established a phase transition at $p = \frac{\log n}{n}$ for this model. We refine the critical value to $p = \frac{\log n - \log \log n }{n}$ and identify the critical window of order $Θ(1/n)$. |
| title | A phase transition in Erdős-Barak random graphs |
| topic | Probability Combinatorics Statistics Theory |
| url | https://arxiv.org/abs/2512.05756 |