On the number of real roots of a random algebraic equation

Journal of the Australian Mathematical Society

D. Pratihari¹ 

[1]R. K. Panda

关键词: 60 B 99;   

DOI  :  10.1017/S1446788700037009

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

Let Nn(ω) be the number of real roots of the random algebraic equation Σnv = 0 avξv (ω)xv = 0, where the ξv(ω)'s are independent, identically distributed random variables belonging to the domain of attraction of the normal law with mean zero and P{ξv(ω) ≠ 0} > 0; also the av 's are nonzero real numbers such that (kn/tn) = 0(log n) where kn = max0≤v≤n |av| and tn = min0≤v≤n |av|. It is shown that for any sequence of positive constants (εn, n ≥ 0) satisfying εn → 0 and ε2nlog n → ∞ there is a positive constant μ so thatfor all n0 sufficiently large.

【 授权许可】

Unknown