scholarly journals Real roots near the unit circle of random polynomials

2021 ◽  
pp. 1
Author(s):  
Marcus Michelen
Keyword(s):  
Unit Circle ◽  
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.

scholarly journals The zeros of random polynomials cluster uniformly near the unit circle

2008 ◽  
Vol 144 (3) ◽  
pp. 734-746 ◽  
Author(s):  
C. P. Hughes ◽  
A. Nikeghbali
Keyword(s):  
Unit Circle ◽  
Asymptotic Distribution ◽  
Random Polynomials ◽  
Famous Result ◽  
Distribution Of Roots ◽  
General Conditions

AbstractIn this paper we deduce a universal result about the asymptotic distribution of roots of random polynomials, which can be seen as a complement to an old and famous result of Erdős and Turan. More precisely, given a sequence of random polynomials, we show that, under some very general conditions, the roots tend to cluster near the unit circle, and their angles are uniformly distributed. The method we use is deterministic: in particular, we do not assume independence or equidistribution of the coefficients of the polynomial.

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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