A phase transition in Erdős-Barak random graphs

Fuente: arXiv
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Main Authors: Blanchard, Gilles, Curien, Nicolas, Krause, Klara, Reisach, Alexander
Format: Preprint
Published: 2025
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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