Real almost zeros of random polynomials with complex coefficients | Zendy

K. Farahmand | Zendy; Alexander Grigorash | Zendy; P. Flood | Zendy

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Real almost zeros of random polynomials with complex coefficients

Author(s) -

K. Farahmand,

Alexander Grigorash,

P. Flood

Publication year - 2005

Publication title -

international journal of stochastic analysis

Language(s) - English

Resource type - Journals

eISSN - 2090-3340

pISSN - 2090-3332

DOI - 10.1155/jamsa.2005.195

Subject(s) - mathematics , algebraic number , polynomial , bounded function , zero (linguistics) , expected value , value (mathematics) , gaussian , discrete mathematics , combinatorics , mathematical analysis , statistics , philosophy , linguistics , physics , quantum mechanics

We present a simple formula for the expected number of times that a complex-valued Gaussian stochastic process has a zero imaginary part and the absolute value of its real part is bounded by a constant value M. We show that only some mild conditions on the stochastic process are needed for our formula to remain valid. We further apply this formula to a random algebraic polynomial with complex coefficients. We show how the above expected value in the case of random algebraic polynomials varies for different behaviour of M

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