Aggregate convergence laws for uniform distributions on restricted graph classes

Establish whether the first-order convergence results known for uniform distributions over restricted sparse graph classes extend to real-valued aggregate logics with averaging operators.

Background

The paper’s results concern Erdős–Rényi distributions, while related first-order convergence laws are known for uniform distributions over several restricted graph classes, including sparse graph classes. The authors do not analyze whether those distribution-specific convergence phenomena persist when first-order logic is extended with aggregation, and explicitly leave this possibility unresolved.