Mean number of real zeros of a random hyperbolic polynomial
2000 ◽
Vol 23
(5)
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pp. 335-342
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Keyword(s):
The Mean
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Consider the random hyperbolic polynomial,f(x)=1pa1coshx+⋯+np×ancoshnx, in whichnandpare integers such thatn≥2, p≥0, and the coefficientsak(k=1,2,…,n)are independent, standard normally distributed random variables. Ifνnpis the mean number of real zeros off(x), then we prove thatνnp=π−1 logn+O{(logn)1/2}.
1997 ◽
Vol 10
(1)
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pp. 67-70
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1995 ◽
Vol 8
(3)
◽
pp. 299-317
1998 ◽
Vol 21
(2)
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pp. 347-350
2015 ◽
Vol 2015
◽
pp. 1-7
2004 ◽
Vol 2004
(63)
◽
pp. 3389-3395
Keyword(s):
1990 ◽
Vol 49
(1)
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pp. 149-160
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1997 ◽
Vol 10
(3)
◽
pp. 257-264
1968 ◽
Vol 64
(3)
◽
pp. 721-730
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1999 ◽
Vol 22
(3)
◽
pp. 579-586