K. Farahmand, P. Hannigan, "Level crossings and turning points of random hyperbolic polynomials", International Journal of Mathematics and Mathematical Sciences, vol. 22, Article ID 957474, 8 pages, 1999. https://doi.org/10.1155/S0161171299225793
Level crossings and turning points of random hyperbolic polynomials
In this paper, we show that the asymptotic estimate for the expected number of -level crossings of a random hyperbolic polynomial , where are independent normally distributed random variables with mean zero and variance one, is . This result is true for all independent of , provided . It is also shown that the asymptotic estimate of the expected number of turning points for the random polynomial , with as before, is also .
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