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How random is the characteristic polynomial of a random matrix ?

Published online by Cambridge University Press:  24 October 2008

Jennie C. Hansen  and
Eric Schmutz
Jennie C. Hansen
Affiliation:
Actuarial Mathematics and Statistics Department, Heriot-Watt University, Edinburgh, Scotland
Eric Schmutz
Affiliation:
Mathematics and Computer Science Department, Drexel University, Philadelphia, PA 19104, USA
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Abstract

Every monic, degree n polynomial in Fq[x;] is the characteristic polynomial of at least one n × n matrix (with entries in the finite field Fq), but they do not appear with equal frequency. There is no a priori reason that the characteristic polynomial of a typical matrix should resemble a typical monic degree n polynomial. Nevertheless, we prove a precise version of the following heuristic statement: ‘Excepting its small factors, the characteristic polynomial of a random matrix is random.’

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 114 , Issue 3 , November 1993 , pp. 507 - 515
Copyright
Copyright © Cambridge Philosophical Society 1993

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