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Creators/Authors contains: "Cook, Nicholas A"

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  1. ; (, The Annals of Applied Probability)
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  2. ; ; (, Duke Mathematical Journal)
    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 Erdo ̋s–Rényi hypergraph for any fixed r≥2, generalizing and improving on previous results for the Erdo ̋s–Rényi 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. 
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  3. ; ; ; (, International Mathematics Research Notices)
    Abstract We give a new proof of a recent resolution [18] by Michelen and Sahasrabudhe of a conjecture of Shepp and Vanderbei [19] that the moduli of roots of Gaussian Kac polynomials of degree $$n$$, centered at $$1$$ and rescaled by $n^2$, should form a Poisson point process. We use this new approach to verify a conjecture from [18] that the Poisson statistics are in fact universal. 
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