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arXiv · 2601.13966

Sample Complexity of Correlation Detection in Erd\H{o}s-R\'enyi graphs

Dong Huang·Pengkun Yang
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Abstract

In this paper, we study correlation detection problem between a pair of Erd\H{o}s-R\'enyi graphs. Under the null hypothesis, the two graphs are independent, whereas under the alternative, they are edge-correlated through a latent permutation. We consider the partial-observation setting in which only an induced subgraph of each graph is sampled, and determine the sharp information-theoretic threshold for the sample size, including its leading constant. We also establish a general conditional second moment principle and identify a continuous transition in the sharp threshold constant across two different regimes.

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Dong Huang, Pengkun Yang. 2026-01-20. Sample Complexity of Correlation Detection in Erd\H{o}s-R\'enyi graphs. https://arxiv.org/abs/2601.13966

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