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On the number of real roots of a random algebraic equation

Part of: Probability theory on algebraic and topological structures

Published online by Cambridge University Press:  09 April 2009

D. Pratihari ,
R. K. Panda  and
B. P. Pattanaik
D. Pratihari
Affiliation:
College of Basic Sciences & HumanitiesBhubaneswar - 751 003, Orissa, INDIA
R. K. Panda
Affiliation:
College of Basic Sciences & HumanitiesBhubaneswar - 751 003, Orissa, INDIA
B. P. Pattanaik
Affiliation:
College of Basic Sciences & HumanitiesBhubaneswar - 751 003, Orissa, INDIA
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Abstract

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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 that for all n0 sufficiently large.

Keywords

Independentidentically distributed random variablesrandom algebraic equationreal rootsdomain of attraction of the normal lawslowly varying function.

MSC classification

Secondary: 60B99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 54 , Issue 1 , February 1993 , pp. 86 - 96
Copyright
Copyright © Australian Mathematical Society 1993

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