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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2 Pith papers cite this work. Polarity classification is still indexing.
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2026 2representative citing papers
Exact Procrustes matching of n Gaussian vectors in d≥polylog(n) dimensions is achievable in polynomial time whenever the correlation satisfies ρ²>√α≈0.58, via counting wide trees.
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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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High-Dimensional Procrustes Matching via Tree Counts
Exact Procrustes matching of n Gaussian vectors in d≥polylog(n) dimensions is achievable in polynomial time whenever the correlation satisfies ρ²>√α≈0.58, via counting wide trees.