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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

How many eigenvalues of a random symmetric tensor are real?


Author: Paul Breiding
Journal: Trans. Amer. Math. Soc. 372 (2019), 7857-7887
MSC (2010): Primary 15A18, 62H99
DOI: https://doi.org/10.1090/tran/7910
Published electronically: September 6, 2019
MathSciNet review: 4029684
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Abstract: This article answers a question posed by Draisma and Horobet, who asked for a closed formula for the expected number of real eigenvalues of a random real symmetric tensor drawn from the Gaussian distribution relative to the Bombieri norm. This expected value is equal to the expected number of real critical points on the unit sphere of a Kostlan polynomial. We also derive an exact formula for the expected absolute value of the determinant of a matrix from the Gaussian Orthogonal Ensemble.


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Paul Breiding
Affiliation: Technische Universität Berlin, Straße des 17. Juni 136, 10623 Berlin, Germany

DOI: https://doi.org/10.1090/tran/7910
Received by editor(s): February 13, 2019
Published electronically: September 6, 2019
Additional Notes: The author was partially supported by DFG research grant BU 1371/2-2.
Article copyright: © Copyright 2019 American Mathematical Society