Geodesic
An example of a random polynomial with unusual behavior of roots
Teoriâ veroâtnostej i ee primeneniâ, Tome 50 (2005) no. 3, pp. 549-555

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This paper constructs an example of random polynomials of order $n=1,2,\dots$ with independent identically distributed coefficients whose average number of real zeros is less than nine for all $n$. The average number $n/2+o(1)$ of complex zeros is concentrated near zero and the same number goes to infinity as $n\to\infty$.
Keywords: random polynomials, average number of real zeros. 
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     author = {D. N. Zaporozhets},
     title = {An example of a random polynomial with unusual behavior of roots},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {549--555},
     publisher = {mathdoc},
     volume = {50},
     number = {3},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2005_50_3_a7/}
}
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D. N. Zaporozhets. An example of a random polynomial with unusual behavior of roots. Teoriâ veroâtnostej i ee primeneniâ, Tome 50 (2005) no. 3, pp. 549-555. http://geodesic.mathdoc.fr/item/TVP_2005_50_3_a7/