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arXiv · 2008.01223

The characteristic polynomial of a random matrix

Sean Eberhard
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Abstract

Form an $n \times n$ matrix by drawing entries independently from $\{\pm1\}$ (or another fixed nontrivial finitely supported distribution in $\mathbf{Z}$) and let $\phi$ be the characteristic polynomial. Conditionally on the extended Riemann hypothesis, with high probability $\phi$ is irreducible and $\mathrm{Gal}(\phi) \geq A_n$.

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Sean Eberhard. 2020-08-03. The characteristic polynomial of a random matrix. https://doi.org/10.1007/s00493-020-4657-0

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