RT - Journal Article
T1 - On Classifications of Random Polynomials
JF - srtc-jsri
YR - 2004
JO - srtc-jsri
VO - 1
IS - 1
UR - http://jsri.srtc.ac.ir/article-1-135-en.html
SP - 1
EP - 12
K1 - number of real zeros
K1 - real roots
K1 - random algebraic polynomials
K1 - trigonometric polynomials
K1 - binomial coefficients
K1 - Kac-Rice formula
K1 - non-identical random variables
K1 - complex roots.
AB - Let $ a_0 (omega), a_1 (omega), a_2 (omega), dots, a_n (omega)$ be a sequence of independent random variables defined on a fixed probability space $(Omega, Pr, A)$. There are many known results for the expected number of real zeros of a polynomial $ a_0 (omega) psi_0(x)+ a_1 (omega)psi_1 (x)+, a_2 (omega)psi_2 (x)+ dots + a_n (omega)psi_n (x)$ where $ psi_j(x)$ , j=0.1.2...,n is a specific function of x. In this paper we highlight different characteristics arising for the random polynomial dictated by assuming different values for $ psi_j(x)$. Then we are able to classify random polynomials into three classes each of which share common properties. Although, we are mainly concerned with the number of real roots we also study the density of complex roots generated by assuming complex random coefficients for polynomials.
LA eng
UL http://jsri.srtc.ac.ir/article-1-135-en.html
M3 10.18869/acadpub.jsri.1.1.1
ER -