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Free, publicly-accessible full text available December 15, 2025
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Abstract In the anisotropic random geometric graph model, vertices correspond to points drawn from a high‐dimensional Gaussian distribution and two vertices are connected if their distance is smaller than a specified threshold. We study when it is possible to hypothesis test between such a graph and an Erdős‐Rényi graph with the same edge probability. If is the number of vertices and is the vector of eigenvalues, Eldan and Mikulincer, Geo. Aspects Func. Analysis: Israel seminar, 2017 shows that detection is possible when and impossible when . We show detection is impossible when , closing this gap and affirmatively resolving the conjecture of Eldan and Mikulincer, Geo. Aspects Func. Analysis: Israel seminar, 2017.more » « less
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