Aggregate convergence laws for root-growth Erdős–Rényi graphs

Establish convergence laws for the averaging logic with global mean, local mean, supremum, and Lipschitz connectives on Erdős–Rényi random featured graphs in the root-growth regimes with edge probability n^{-\alpha} for 0<\alpha<1.

Background

The paper studies convergence of real-valued logical terms containing averaging operators on dense and linear-sparse Erdős–Rényi random featured graphs. It notes that, for first-order logic, rational root-growth exponents can prevent convergence, whereas irrational exponents yield a zero-one law. Because the proposed term language extends first-order logic, the authors do not establish convergence in all root-growth regimes and explicitly leave these cases unresolved.