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The Characteristic Polynomial of a Random Matrix
Combinatorica ( IF 1.0 ) Pub Date : 2022-03-14 , DOI: 10.1007/s00493-020-4657-0 Sean Eberhard 1
中文翻译:
随机矩阵的特征多项式
更新日期:2022-03-14
Combinatorica ( IF 1.0 ) Pub Date : 2022-03-14 , DOI: 10.1007/s00493-020-4657-0 Sean Eberhard 1
Affiliation
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.
中文翻译:
随机矩阵的特征多项式
通过独立于 {±1}(或Z中的另一个固定非平凡有限支持分布)绘制条目来形成n × n矩阵,并令φ为特征多项式。我们在扩展黎曼假设的条件下证明了φ是不可约的且 Gal( φ ) ≥ A n的概率很高。