On random algebraic polynomials
نویسندگان
چکیده
منابع مشابه
On Algebraic Polynomials with Random Coefficients
The expected number of real zeros and maxima of the curve representing algebraic polynomial of the form a0 (n−1 0 )1/2 + a1 (n−1 1 )1/2 x + a2 (n−1 2 )1/2 x2 + · · · + an−1 (n−1 n−1 )1/2 xn−1 where aj , j = 0, 1, 2, . . . , n − 1, are independent standard normal random variables, are known. In this paper we provide the asymptotic value for the expected number of maxima which occur below a given...
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The expected number of real zeros of the polynomial of the form a0 a1x a2x · · · anx, where a0, a1, a2, . . . , an is a sequence of standard Gaussian random variables, is known. For n large it is shown that this expected number in −∞,∞ is asymptotic to 2/π logn. In this paper, we show that this asymptotic value increases significantly to √ n 1 when we consider a polynomial in the form a0 ( n 0 ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1999
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-99-04912-6