The Characteristic Polynomial of a Random Matrix View Full Text


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Article Info

DATE

2022-03-14

AUTHORS

Sean Eberhard

ABSTRACT

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.

PAGES

1-37

References to SciGraph publications

  • 2017-03-24. Random matrices have simple spectrum in COMBINATORICA
  • 2018-06-23. Low-Degree Factors of Random Polynomials in JOURNAL OF THEORETICAL PROBABILITY
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    http://scigraph.springernature.com/pub.10.1007/s00493-020-4657-0

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    http://dx.doi.org/10.1007/s00493-020-4657-0

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