Expected density of complex zeros of random hyperbolic polynomials

There are many known asymptotic estimates for the expected number of real zeros of polynomial H n ( z) = η 1 cosh ζ z + η 2 cosh 2ζ z + ⋯ + η n cosh nζ z, where η j , j = 1, 2, 3, …, n is a sequence of independent random variables. This paper provides the asymptotic formula for the expected density...

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Vydáno v:	Applied mathematics letters Ročník 15; číslo 4; s. 389 - 393
Hlavní autoři:	Farahmand, K., Grigorash, A.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Oxford Elsevier Ltd 01.05.2002 Elsevier
Témata:	Adler's theorem Complex roots Coordinate transform Density of zeros Exact sciences and technology Jacobian of transformation Mathematics Number of complex zeros Random algebraic polynomials Random hyperbolic polynomials Random trigonometric polynomials Real roots Sciences and techniques of general use Density of zeros Real roots Adler's theorem Random hyperbolic polynomials Random algebraic polynomials Coordinate transform Complex roots Random trigonometric polynomials Jacobian of transformation Number of complex zeros
ISSN:	0893-9659, 1873-5452
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Popis
Shrnutí:	There are many known asymptotic estimates for the expected number of real zeros of polynomial H n ( z) = η 1 cosh ζ z + η 2 cosh 2ζ z + ⋯ + η n cosh nζ z, where η j , j = 1, 2, 3, …, n is a sequence of independent random variables. This paper provides the asymptotic formula for the expected density of complex zeros of H n ( z), where η j = a j + ib j and a j and b j , 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.
ISSN:	0893-9659 1873-5452
DOI:	10.1016/S0893-9659(01)00148-3