:: Volume 1, Issue 1 (9-2004) ::
JSRI 2004, 1(1): 1-12 Back to browse issues page
On Classifications of Random Polynomials
K. Farahmand *
, k.farahmand@uist.ac.uk
Abstract:   (2442 Views)

 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.

Keywords: number of real zeros, real roots, random algebraic polynomials, trigonometric polynomials, binomial coefficients, Kac-Rice formula, non-identical random variables, complex roots.
Full-Text [PDF 773 kb]   (539 Downloads)    
Type of Study: Research | Subject: General
Received: 2016/02/9 | Accepted: 2016/02/9 | Published: 2016/02/9



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Volume 1, Issue 1 (9-2004) Back to browse issues page