scholarly journals Real roots of random polynomials with coefficients of polynomial growth: a comparison principle and applications

2021 ◽  
Vol 26 (none) ◽  
Author(s):  
Yen Q. Do
Keyword(s):  
Comparison Principle ◽  
Polynomial Growth ◽  
Random Polynomials ◽  
Real Roots

scholarly journals Real roots of random polynomials: expectation and repulsion

2015 ◽  
Vol 111 (6) ◽  
pp. 1231-1260 ◽  
Author(s):  
Yen Do ◽  
Hoi Nguyen ◽  
Van Vu
Keyword(s):  
Random Polynomials ◽  
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.

Random Polynomials with Real Roots: 10660

1999 ◽  
Vol 106 (5) ◽  
pp. 477 ◽  
Author(s):  
Colin L. Mallows ◽  
Kenneth Schilling
Keyword(s):  
Random Polynomials ◽  
Real Roots
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