The characteristic polynomial of a random matrix

Sean Eberhard*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


Form an n × n matrix by drawing entries independently from {±1} (or another fixed nontrivial finitely supported distribution in Z) and let φ be the characteristic polynomial. We show, conditionally on the extended Riemann hypothesis, that with high probability φ is irreducible and Gal(φ) ≥ An.

Original languageEnglish
Pages (from-to)491-527
Number of pages37
Issue number4
Early online date14 Mar 2022
Publication statusPublished - Aug 2022
Externally publishedYes

Bibliographical note

Funding Information:
The author has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 803711).

Publisher Copyright:
© 2022, János Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg.

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Computational Mathematics


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