2 problems

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Gilmer–Kopparty's local central limit conjecture for subgraph counts
Gilmer–Kopparty's conjecture. A local central limit theorem should hold for $X_H$ .
Conjectureopenlocal-central-limit-theorems random-graphs subgraph-countsarXiv posted 2 days ago
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Local central limit conjecture for the hard-core model
Local central limit conjecture. If $\lambda<\lambda_c(\Delta)$ , then
Conjectureopenhard-core-model local-central-limit-theorems statistical-physicsarXiv posted 2 days ago

Gilmer–Kopparty's local central limit conjecture for subgraph counts