Individual phases in phase-coexisting exponential random graph models satisfy an approximate FKG inequality, enabling central limit theorems within each phase.
Metastable mixing of markov chains: Efficiently sampling low temperature exponential random graphs.The Annals of Applied Probability, 34(1A):517–554, 2024
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Approximate FKG inequalities for phase-bound spin systems, with applications to central limit theorems for exponential random graphs
Individual phases in phase-coexisting exponential random graph models satisfy an approximate FKG inequality, enabling central limit theorems within each phase.