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REGULARITY METHOD AND LARGE DEVIATION PRINCIPLES FOR THE ERDŐS–RÉNYI HYPERGRAPH
Publication
, Journal Article
Cook, NA; Dembo, A; Pham, HT
Published in: Duke Mathematical Journal
April 1, 2024
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.
Duke Scholars
Published In
Duke Mathematical Journal
DOI
ISSN
0012-7094
Publication Date
April 1, 2024
Volume
173
Issue
5
Start / End Page
873 / 946
Related Subject Headings
- General Mathematics
- 4904 Pure mathematics
- 0101 Pure Mathematics
Citation
APA
Chicago
ICMJE
MLA
NLM
Cook, N. A., Dembo, A., & Pham, H. T. (2024). REGULARITY METHOD AND LARGE DEVIATION PRINCIPLES FOR THE ERDŐS–RÉNYI HYPERGRAPH. Duke Mathematical Journal, 173(5), 873–946. https://doi.org/10.1215/00127094-2023-0029
Cook, N. A., A. Dembo, and H. T. Pham. “REGULARITY METHOD AND LARGE DEVIATION PRINCIPLES FOR THE ERDŐS–RÉNYI HYPERGRAPH.” Duke Mathematical Journal 173, no. 5 (April 1, 2024): 873–946. https://doi.org/10.1215/00127094-2023-0029.
Cook NA, Dembo A, Pham HT. REGULARITY METHOD AND LARGE DEVIATION PRINCIPLES FOR THE ERDŐS–RÉNYI HYPERGRAPH. Duke Mathematical Journal. 2024 Apr 1;173(5):873–946.
Cook, N. A., et al. “REGULARITY METHOD AND LARGE DEVIATION PRINCIPLES FOR THE ERDŐS–RÉNYI HYPERGRAPH.” Duke Mathematical Journal, vol. 173, no. 5, Apr. 2024, pp. 873–946. Scopus, doi:10.1215/00127094-2023-0029.
Cook NA, Dembo A, Pham HT. REGULARITY METHOD AND LARGE DEVIATION PRINCIPLES FOR THE ERDŐS–RÉNYI HYPERGRAPH. Duke Mathematical Journal. 2024 Apr 1;173(5):873–946.
![Journal cover image](https://secure.syndetics.com/index.aspx?isbn=/lc.gif&issn=0012-7094&client=dukeuniv)
Published In
Duke Mathematical Journal
DOI
ISSN
0012-7094
Publication Date
April 1, 2024
Volume
173
Issue
5
Start / End Page
873 / 946
Related Subject Headings
- General Mathematics
- 4904 Pure mathematics
- 0101 Pure Mathematics