Publications [#377238] of Nicholas A Cook

Papers Published

1. Cook, NA; Dembo, A; Pham, HT, REGULARITY METHOD AND LARGE DEVIATION PRINCIPLES FOR THE ERDŐS–RÉNYI HYPERGRAPH, Duke Mathematical Journal, vol. 173 no. 5 (April, 2024), pp. 873-946 [doi]
   (last updated on 2025/03/13)

   Abstract:
   We develop a quantitative large deviations theory for random hypergraphs, which rests on tensor decomposition and counting lemmas under a novel family of cut-type norms. As our main application, we obtain sharp asymptotics for joint upper and lower tails of homomorphism counts in the r-uniform Erdős–Rényi hypergraph for any fixed r ≥ 2, generalizing and improving on previous results for the Erdős–Rényi graph (r D 2). The theory is sufficiently quantitative to allow the density of the hypergraph to vanish at a polynomial rate, and additionally yields tail asymptotics for other nonlinear functionals, such as induced homomorphism counts.