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On the Upper Bound of the Number of Real Roots of a Random Algebraic Equation with Infinite Variance
Author(s) -
Samal G.,
Mishra M. N.
Publication year - 1973
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-6.4.598
Subject(s) - upper and lower bounds , mathematics , citation , algebraic number , variance (accounting) , combinatorics , statistics , computer science , library science , mathematical analysis , accounting , business
Let N„ be the number of real roots of a random algebraic equation 2o avSvx*=0, where fv's are independent random variables with common characteristic functionexp( —C|f I"), C being a positive constant, a^l and a0, a¡, ■ ■ ■ , a„ are nonzero real numbers. Let K„=maxoâvs„ lav|, r„=minoSvSn |av|. If A„= H log n/log((«r„//„)Iog n), then (i) Pr{(AyA„) £ p.) < ß -—j log(((c„//„)log n)(log h)"-1 if 1 ̂ a<2 and 2, provided («:„//„) = o(log n). 00 Prfsup^^} og((Clo)°iog« )} if a>l, provided log(/<:„/0=o(Iog «). It may be remarked that the coefficients av£v's in the above equation are not identically distributed.