On the Average Number of Real Roots of a Random Algebraic Equation

Farahmand, Kambiz

Ann. Probab., Tome 14 (1986) no. 4, p. 702-709 / Harvested from Project Euclid

Résumé

There are many known asymptotic estimates of the expected number of zeros of a polynomial of degree $n$ with independent random coefficients, for $n \rightarrow \infty$. The present paper provides an estimate of the expected number of times that such a polynomial assumes the real value $K$, where $K$ is not necessarily zero. The coefficients are assumed to be normally distributed. It is shown that the results are valid even for $K \rightarrow \infty$, as long as $K = O(\sqrt n)$.

Publié le : 1986-04-14
Classification: 60H, Number of real roots, Kac-Rice formula, random algebraic equation

@article{1176992539,
     author = {Farahmand, Kambiz},
     title = {On the Average Number of Real Roots of a Random Algebraic Equation},
     journal = {Ann. Probab.},
     volume = {14},
     number = {4},
     year = {1986},
     pages = { 702-709},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176992539}
}

Farahmand, Kambiz. On the Average Number of Real Roots of a Random Algebraic Equation. Ann. Probab., Tome 14 (1986) no. 4, pp.  702-709. http://gdmltest.u-ga.fr/item/1176992539/