Regularity method and large deviation principles for the Erdős--Rényi hypergraph
Publication
, Journal Article
Cook, NA; Dembo, A; Pham, HT
February 17, 2021
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.
Duke Scholars
Publication Date
February 17, 2021
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Cook, N. A., Dembo, A., & Pham, H. T. (2021). Regularity method and large deviation principles for the
Erdős--Rényi hypergraph.
Cook, Nicholas A., Amir Dembo, and Huy Tuan Pham. “Regularity method and large deviation principles for the
Erdős--Rényi hypergraph,” February 17, 2021.
Cook NA, Dembo A, Pham HT. Regularity method and large deviation principles for the
Erdős--Rényi hypergraph. 2021 Feb 17;
Cook, Nicholas A., et al. Regularity method and large deviation principles for the
Erdős--Rényi hypergraph. Feb. 2021.
Cook NA, Dembo A, Pham HT. Regularity method and large deviation principles for the
Erdős--Rényi hypergraph. 2021 Feb 17;
Publication Date
February 17, 2021