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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Veröffentlicht in:Applied mathematics letters Jg. 15; H. 4; S. 389 - 393
Hauptverfasser: Farahmand, K., Grigorash, A.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Oxford Elsevier Ltd 01.05.2002
Elsevier
Schlagworte:
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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Zusammenfassung: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