The Characteristic Polynomial of a Random Matrix

被引：7

作者：

Eberhard, Sean ^{[1
]}

机构：

[1] Ctr Math Sci, Wilberforce Rd, Cambridge CB3 0WB, England

来源：

COMBINATORICA | 2022年 / 42卷 / 04期

基金：

欧洲研究理事会;

关键词：

11M50; 15B52; SINGULARITY;

D O I：

10.1007/s00493-020-4657-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Form an n x n matrix by drawing entries independently from {+/- 1} (or another fixed nontrivial finitely supported distribution in Z) and let phi be the characteristic polynomial. We show, conditionally on the extended Riemann hypothesis, that with high probability phi is irreducible and Gal(phi) >= A(n).

引用

下载

页码：491 / 527

页数：37

共 50 条

[1] The Characteristic Polynomial of a Random Matrix
Sean Eberhard
Combinatorica, 2022, 42 : 491 - 527
[2] On the Characteristic Polynomial¶ of a Random Unitary Matrix
C. P. Hughes
J. P. Keating
Neil O'Connell
Communications in Mathematical Physics, 2001, 220 : 429 - 451
[3] On the characteristic polynomial of a random unitary matrix
Hughes, C.P.
Keating, J.P.
O'Connell, Neil
HP Laboratories Technical Report, 2000, BRIMS (17):
[4] The characteristic polynomial of a random permutation matrix
Hambly, B.M., 2000, Hewlett Packard Laboratories (BRIMS):
[5] On the characteristic polynomial of a random unitary matrix
Hughes, CP
Keating, JP
O'Connell, N
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2001, 220 (02) : 429 - 451
[6] The characteristic polynomial of a random permutation matrix
Hambly, BM
Keevash, P
O'Connell, N
Stark, D
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2000, 90 (02) : 335 - 346
[7] HOW RANDOM IS THE CHARACTERISTIC POLYNOMIAL OF A RANDOM-MATRIX
HANSEN, JC
SCHMUTZ, E
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1993, 114 : 507 - 515
[8] Maximum of the Characteristic Polynomial for a Random Permutation Matrix
Cook, Nicholas
Zeitouni, Ofer
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2020, 73 (08) : 1660 - 1731
[9] On the moments of the characteristic polynomial of a Ginibre random matrix
Webb, Christian
Wong, Mo Dick
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2019, 118 (05) : 1017 - 1056
[10] The characteristic polynomial of a random permutation matrix at different points
Dang, K.
Zeindler, D.
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2014, 124 (01) : 411 - 439

← 1 2 3 4 5 →