Localization conjecture for differences under optimal ERGM couplings

Let two random graphs be sampled under a coupling of an ERGM and a corresponding Erdős–Rényi model. Localization conjecture. For certain ERGM specifications, under some coupling with a corresponding Erdős–Rényi model, the difference between the two sampled graphs is typically constrained to a localized region. The source presents this as a vague question for future work and gives no precise definition of “typically” or “localized region.”