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Expected density of complex zeros of random hyperbolic polynomials

โœ Scribed by K. Farahmand; A. Grigorash

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
335 KB
Volume
15
Category
Article
ISSN
0893-9659

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โœฆ Synopsis

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 zerce of Hn (z), where nj = ej + 1b.j and oj and bj, j = 1,2,3, . . . , n are sequences of independent normally distributed random variables. It is shown that this asymptotic formula for the density of complex zeros remains invariant for other types of polynomials, for instance random trigonometric polynomials, previously studied. @ 2002 Elsevier Science Ltd. All rights reserved. Keywords-Number of complex zeroe, Real roote, Complex roots, Random hyperbolic polynomials, Random trigonometric polynomials, Random algebraic polynomials, Jacobian of transformation, Adler's theorem, Coordinate transform, Density of zeros.

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