## How many eigenvalues of a random symmetric tensor are real?

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- by Paul Breiding PDF
- Trans. Amer. Math. Soc.
**372**(2019), 7857-7887 Request permission

## 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.## References

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## Additional Information

**Paul Breiding**- Affiliation: Technische Universität Berlin, Straße des 17. Juni 136, 10623 Berlin, Germany
- MR Author ID: 1151466
- 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.
- © Copyright 2019 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**372**(2019), 7857-7887 - MSC (2010): Primary 15A18, 62H99
- DOI: https://doi.org/10.1090/tran/7910
- MathSciNet review: 4029684