Publications [#361355] of Nicholas A Cook

Papers Published

1. Cook, NA; Dembo, A; Pham, HT, Regularity method and large deviation principles for the Erdős--Rényi hypergraph (February, 2021)
   (last updated on 2024/04/19)

   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 Erd\H{o}s--R\'enyi hypergraph for any fixed $r\ge 2$, generalizing and improving on previous results for the Erd\H{o}s--R\'enyi graph ($r=2$). 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.