Real zeros of random algebraic polynomials with
binomial elements
2006 ◽
Vol 2006
◽
pp. 1-6
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Keyword(s):
This paper provides an asymptotic estimate for the expected number of real zeros of a random algebraic polynomial a0+a1x+a2x2+…+an−1xn−1. The coefficients aj(j=0,1,2,…,n−1) are assumed to be independent normal random variables with mean zero. For integers m and k=O(logn)2 the variances of the coefficients are assumed to have nonidentical value var(aj)=(k−1j−ik), where n=k⋅m and i=0,1,2,…,m−1. Previous results are mainly for identically distributed coefficients or when var(aj)=(nj). We show that the latter is a special case of our general theorem.
2004 ◽
Vol 2004
(63)
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pp. 3389-3395
Keyword(s):
2003 ◽
Vol 16
(3)
◽
pp. 249-255
◽
1998 ◽
Vol 21
(2)
◽
pp. 347-350
1997 ◽
Vol 10
(1)
◽
pp. 57-66
◽
2008 ◽
Vol 85
(1)
◽
pp. 81-86
◽
1984 ◽
Vol 2
(4)
◽
pp. 431-436
◽
Keyword(s):
2008 ◽
Vol 2008
◽
pp. 1-8
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2009 ◽
Vol 2009
◽
pp. 1-6
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2001 ◽
Vol 14
(3)
◽
pp. 265-274
◽