There are many known asymptotic estimates for the expected number of real zeroe of polynomial &(z) = rn coeh CL + ~2 coeh 2(z + . . . +q,,ccehn<z, where qj, j = 1,2,3 ,..., n ie a sequence of independent random variables. This paper provides the asymptotic formula for the expected density of complex
Expected density of complex roots of random polynomials
β Scribed by K. Farahmand; A. Grigorash
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 307 KB
- Volume
- 47
- Category
- Article
- ISSN
- 0362-546X
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## By using the technique proposed in ), Trans. Amer. Math. Soc. 349, 2427 -2441] , we derive an exact formula for the mean number of complex roots of a complex random polynomial. The explicit evaluation of the average density is obtained in the case of multivariate normal coe cients and its co
This paper, for any constant K, provides an exact formula for the average density of the distribution of the complex roots of equation q z q z 2 0 1 2 n y 1 Γ 4 ny1 Γ 4 ny1 qΠΈΠΈΠΈ q z s K where s a q ib and a and b are sequences of independent identically and normally distributed random variables and