Large level crossings of a random polynomial
1988 ◽
Vol 1
(4)
◽
pp. 259-269
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Keyword(s):
We know the expected number of times that a polynomial of degree n with independent random real coefficients asymptotically crosses the level K, when K is any real value such that (K2/n)→0 as n→∞. The present paper shows that, when K is allowed to be large, this expected number of crossings reduces to only one. The coefficients of the polynomial are assumed to be normally distributed. It is shown that it is sufficient to let K≥exp(nf) where f is any function of n such that f→∞ as n→∞.
1999 ◽
Vol 22
(3)
◽
pp. 579-586
1995 ◽
Vol 58
(1)
◽
pp. 39-46
2002 ◽
Vol 15
(1)
◽
pp. 83-88
1997 ◽
Vol 208
(1)
◽
pp. 205-217
1997 ◽
Vol 10
(3)
◽
pp. 257-264
2005 ◽
Vol 23
(6)
◽
pp. 1141-1147
2002 ◽
Vol 30
(2)
◽
pp. 100-106
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Keyword(s):
1989 ◽
Vol 33
(2)
◽
pp. 217-231
◽