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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On the lower bound of the number of real roots of a random algebraic equation with infinite variance. II


Authors: G. Samal and M. N. Mishra
Journal: Proc. Amer. Math. Soc. 36 (1972), 557-563
MSC: Primary 60G99
DOI: https://doi.org/10.1090/S0002-9939-1972-0315785-5
MathSciNet review: 0315785
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Abstract: Let $ {N_n}$ be the number of real roots of a random algebraic equation $ \sum\nolimits_{v = 0}^n {{\xi _v}{x^v} = 0} $ where the $ {\xi _v}$'s are independent random variables with a common characteristic function

$\displaystyle \exp ( - C\vert t{\vert^\alpha }),\quad \alpha > 1,$

and C, a positive constant. Then for $ n > {n_0}$,

$\displaystyle {N_n} > (\mu \log n)/(\log \log n)$

outside a set of measure at most

$\displaystyle \mu '/{\{ \log ((\log {n_0})/(\log \log {n_0}))\} ^{\alpha - 1}}.$


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0315785-5
Keywords: Random equation, infinite variance, real zeros, lower bound
Article copyright: © Copyright 1972 American Mathematical Society

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