On the Distribution of the Number of Real Roots of Random Polynomials

1975 ◽  
Vol 19 (3) ◽  
pp. 461-473 ◽  
Author(s):  
N. B. Maslova
Keyword(s):  
Random Polynomials ◽  
Real Roots ◽  
Number Of Real Roots

scholarly journals On the number of real roots of random polynomials

2016 ◽  
Vol 18 (04) ◽  
pp. 1550052 ◽  
Author(s):  
Hoi Nguyen ◽  
Oanh Nguyen ◽  
Van Vu
Keyword(s):  
Error Term ◽  
Random Polynomials ◽  
True Nature ◽  
Real Roots ◽  
Famous Result ◽  
Long Time ◽  
Number Of Real Roots

Roots of random polynomials have been studied intensively in both analysis and probability for a long time. A famous result by Ibragimov and Maslova, generalizing earlier fundamental works of Kac and Erdős–Offord, showed that the expectation of the number of real roots is [Formula: see text]. In this paper, we determine the true nature of the error term by showing that the expectation equals [Formula: see text]. Prior to this paper, the error term [Formula: see text] has been known only for polynomials with Gaussian coefficients.

scholarly journals On the Lower Bound for the Number of Real Roots of a Random Algebraic Equation

2007 ◽  
Vol 2007 ◽  
pp. 1-8
Author(s):  
Takashi Uno
Keyword(s):  
Lower Bound ◽  
Algebraic Equation ◽  
Random Variables ◽  
Real Roots ◽  
Number Of Real Roots

We estimate a lower bound for the number of real roots of a random alegebraic equation whose random coeffcients are dependent normal random variables.

scholarly journals Asymptotic variance of the number of real roots of random polynomial systems

2018 ◽  
Vol 146 (12) ◽  
pp. 5437-5449 ◽  
Author(s):  
D. Armentano ◽  
J-M. Azaïs ◽  
F. Dalmao ◽  
J. R. León
Keyword(s):  
Asymptotic Variance ◽  
Polynomial Systems ◽  
Random Polynomial ◽  
Real Roots ◽  
Number Of Real Roots
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