Modular statistics for subgraph counts in sparse random graphs
DeMarco, Bobby · Kahn, Jeff · Redlich, Amanda
Original · EN
Answering a question of Kolaitis and Kopparty, we show that, for given integer q>1 and pairwise nonisomorphic connected graphs G₁...Gₖ, if p=p(n) is such that (Gₙ,ₚ Gᵢ)→ 1 ∀ i, then, with ξᵢ the number of copies of Gᵢ in Gₙ,ₚ, (ξ₁...ξₖ) is asymptotically uniformly distributed on Zqᵏ.
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