Proves detection of RGG vs. ER is impossible for d ≫ (n h(p))^3 and d ≥ (1+ε)n, resolving the detection threshold conjecture in the regime p ≳ n^{-2/3}/log n.
Random geometric graphs with smooth kernels: sharp detection threshold and a spectral conjecture.arXiv preprint arXiv:2602.14998,
2 Pith papers cite this work. Polarity classification is still indexing.
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Spectral and SDP algorithms using signed triangle count matrices recover planted triangle-dense subgraphs, with computational threshold at least sqrt(n) for low-degree methods versus information-theoretic threshold at most logarithmic in n.
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Resolution of the Detection Threshold Conjecture for Random Geometric Graphs in the $d>n$ Regime
Proves detection of RGG vs. ER is impossible for d ≫ (n h(p))^3 and d ≥ (1+ε)n, resolving the detection threshold conjecture in the regime p ≳ n^{-2/3}/log n.
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Spectral recovery of a planted triangle-dense subgraph
Spectral and SDP algorithms using signed triangle count matrices recover planted triangle-dense subgraphs, with computational threshold at least sqrt(n) for low-degree methods versus information-theoretic threshold at most logarithmic in n.