Distribution of roots of random real generalized polynomials
نویسندگان
چکیده
منابع مشابه
On the Distribution of Roots of Random Polynomials
In the study of algebraic and numerical properties of polynomials one occasionally introduces the notion of a random polynomial. For example, this chapter was originally motivated by investigations, including [Ki, Re, SS, Sml, Sm2], into the complexity of root-finding algorithms for polynomials. We restrict our attention to central normal measures on spaces of polynomials, i.e., we assume that ...
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Roots of random polynomials have been studied exclusively in both analysis and probability for a long time. A famous result by Ibragimov and Maslova, generalizing earlier fundamental works of Kac and Erdős-Offord, showed that the expectation of the number of real roots is 2 π logn + o(logn). In this paper, we determine the true nature of the error term by showing that the expectation equals 2 π...
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In this article we investigate real roots of real polynomials. By results of M. Kac 8, 9, 10] we know that a polynomial of degree n has in average 2 log n real zeros. See also results of Edelman and Kostlan 5] on the same subject. Some 10 years later Erdds and OOord 7] proved that the mean number of real roots of a random polynomial of degree n with coeecients 1 is again 2 log n: This leads us ...
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Let Pn(x) = ∑n i=0 ξix i be a Kac random polynomial where the coefficients ξi are iid copies of a given random variable ξ. Our main result is an optimal quantitative bound concerning real roots repulsion. This leads to an optimal bound on the probability that there is a real double root. As an application, we consider the problem of estimating the number of real roots of Pn, which has a long hi...
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We study the distribution of the complex roots of random polynomials of degree n with i.i.d. coefficients. Using techniques related to Rice’s treatment of the real roots question, we derive, under appropriate moment and regularity conditions, an exact formula for the average density of this distribution, which yields appropriate limit average densities. Further, using a different technique, we ...
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ژورنال
عنوان ژورنال: Journal of Statistical Physics
سال: 1997
ISSN: 0022-4715,1572-9613
DOI: 10.1007/bf02199115