Tal Hershko

First order distinguishability of sparse random graphs

2024 · arXiv (Cornell University)

We study the problem of distinguishing between two independent samples $\mathbf{G}_n^1,\mathbf{G}_n^2$ of a binomial random graph $G(n,p)$ by first order (FO) sentences. Shelah and Spencer proved that, for a constant $α\in(0,1)$, $G(n,n^{-α})$ obeys FO zero-one …