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Algebraic polynomials with random non-symmetric coefficients

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  • Farahmand, K.
  • Stretch, C.T.

Abstract

This paper provides an asymptotic formula for the expected number of zeros of a polynomial of the form for large n. The coefficients are assumed to be a sequence of independent normally distributed random variables with fixed mean [mu] and variance one. It is shown that for [mu] non-zero this expected number is half of that for [mu]=0. This behavior is similar to that of classical random algebraic polynomials but differs from that of random trigonometric polynomials.

Suggested Citation

  • Farahmand, K. & Stretch, C.T., 2008. "Algebraic polynomials with random non-symmetric coefficients," Statistics & Probability Letters, Elsevier, vol. 78(11), pages 1305-1313, August.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:11:p:1305-1313
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    References listed on IDEAS

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    1. Ramponi, A., 1999. "A note on the complex roots of complex random polynomials," Statistics & Probability Letters, Elsevier, vol. 44(2), pages 181-187, August.
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