Geodesic
What is the Least Expected Number of Real Roots of a Random Polynomial?
Teoriâ veroâtnostej i ee primeneniâ, Tome 53 (2008) no. 1, pp. 40-58

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Let $G_n$ be a random polynomial with coefficients. Denote by $\mathcal{N}(G_n)$ the number of real roots of $G_n$. We find the minimum of $\sup_{n\in{N}}E\mathcal{N}(G_n)$ over different classes of coefficient distributions.
Mots-clés : random polynomial
Keywords: expected number of real roots. 
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     author = {D. N. Zaporozhets and A. I. Nazarov},
     title = {What is the {Least} {Expected} {Number} of {Real} {Roots} of a {Random} {Polynomial?}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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D. N. Zaporozhets; A. I. Nazarov. What is the Least Expected Number of Real Roots of a Random Polynomial?. Teoriâ veroâtnostej i ee primeneniâ, Tome 53 (2008) no. 1, pp. 40-58. http://geodesic.mathdoc.fr/item/TVP_2008_53_1_a2/