On the number of minima of a random polynomial

@article{Dedieu2008OnTN,
  title={On the number of minima of a random polynomial},
  author={Jean-Pierre Dedieu and Gregorio Malajovich},
  journal={J. Complexity},
  year={2008},
  volume={24},
  pages={89-108}
}
We give an upper bound in O(d) for the number of critical points of a normal random polynomial. The number of minima (resp. maxima) is in O(d)Pn, where Pn is the (unknown) measure of the set of symmetric positive matrices in the Gaussian Orthogonal Ensemble GOE(n). Finally, we give a closed form expression for the number of maxima (resp. minima) of a random univariate polynomial, in terms of hypergeometric functions. 
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SHOWING 1-10 OF 12 REFERENCES

On the average number of real roots of a random algebraic equation

  • M. Kac
  • Bull. Am. Math. Soc
  • 1943
Highly Influential
4 Excerpts

Kostlan, How many zeros of a random polynomial are real

  • A. Edelman
  • Bulletin of the AMS,
  • 1995
2 Excerpts

Complexity of Bézout’s Theorem II: Volumes and Probabilities in: Computational Algebraic Geometry, F

  • M. Shub, S. Smale
  • Eyssette and A. Galligo eds., em Progress in…
  • 1993

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