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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4 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
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2026 4representative citing papers
Measurable versions of Whitney's 2-isomorphism theorem are established for locally finite graphings by defining weak isomorphisms that preserve edge measures, cycles, and hyperfinite subgraphs, with rigidity for weakly 3-connected infinitely-ended cases and implementation via countable measurable Wh
Two relational structures are indistinguishable by k-RCR if and only if they receive identical homomorphism counts from every structure of generalised hypertreewidth ≤ k.
Derives the Slepian-Wolf rate region for distributed source coding of connected soft random geometric graphs by proving new entropy limit theorems and asymptotic equipartition properties.
citing papers explorer
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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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Whitney's 2-isomorphism theorem for graphings
Measurable versions of Whitney's 2-isomorphism theorem are established for locally finite graphings by defining weak isomorphisms that preserve edge measures, cycles, and hyperfinite subgraphs, with rigidity for weakly 3-connected infinitely-ended cases and implementation via countable measurable Wh
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Homomorphism Indistinguishability Beyond Graphs: Relational Weisfeiler--Leman and Hypertree Width
Two relational structures are indistinguishable by k-RCR if and only if they receive identical homomorphism counts from every structure of generalised hypertreewidth ≤ k.
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Entropy and Distributed Source Coding of Connected Soft Random Geometric Graphs
Derives the Slepian-Wolf rate region for distributed source coding of connected soft random geometric graphs by proving new entropy limit theorems and asymptotic equipartition properties.