On the number of real roots of random polynomials
2016 ◽
Vol 18
(04)
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pp. 1550052
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Keyword(s):
Roots of random polynomials have been studied intensively in both analysis and probability for a long time. A famous result by Ibragimov and Maslova, generalizing earlier fundamental works of Kac and Erdős–Offord, showed that the expectation of the number of real roots is [Formula: see text]. In this paper, we determine the true nature of the error term by showing that the expectation equals [Formula: see text]. Prior to this paper, the error term [Formula: see text] has been known only for polynomials with Gaussian coefficients.
1974 ◽
Vol 19
(1)
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pp. 35-52
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1975 ◽
Vol 19
(3)
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pp. 461-473
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2007 ◽
Vol 2007
◽
pp. 1-8
2018 ◽
Vol 146
(12)
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pp. 5437-5449
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Keyword(s):
1983 ◽
Vol 1
(2)
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pp. 215-238
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Keyword(s):
1959 ◽
Vol 77
(6)
◽
pp. 670-673
Keyword(s):
1973 ◽
Vol 39
(1)
◽
pp. 184-184
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Keyword(s):