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Free, publicly-accessible full text available December 1, 2025
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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.more » « less
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null (Ed.)Abstract We show that a nearly square independent and identically distributed random integral matrix is surjective over the integral lattice with very high probability. This answers a question by Koplewitz [6]. Our result extends to sparse matrices as well as to matrices of dependent entries.more » « less
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