Modular statistics for subgraph counts in sparse random graphs

Answering a question of Kolaitis and Kopparty, we show that, for given integer $q>1$ and pairwise nonisomorphic connected graphs $G_1...G_k$, if $p=p(n)$ is such that $\Pr(G_{n,p}\supseteq G_i)\to 1$ $\forall i$, then, with $ξ_i$ the number of copies of $G_i$ in $G_{n,p}$, $(ξ_1...ξ_k)$ is asymptotically uniformly distributed on ${\bf Z}_q^k$.

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