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Real Zeros of a Class of Hyperbolic Polynomials with Random Coefficients

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  • Mina Ketan Mahanti
  • Amandeep Singh
  • Lokanath Sahoo

Abstract

We have proved here that the expected number of real zeros of a random hyperbolic polynomial of the form , where is a sequence of standard Gaussian random variables, is . It is shown that the asymptotic value of expected number of times the polynomial crosses the level is also as long as does not exceed , where . The number of oscillations of about will be less than asymptotically only if , where or . In the former case the number of oscillations continues to be a fraction of and decreases with the increase in value of . In the latter case, the number of oscillations reduces to and almost no trace of the curve is expected to be present above the level if log .

Suggested Citation

  • Mina Ketan Mahanti & Amandeep Singh & Lokanath Sahoo, 2015. "Real Zeros of a Class of Hyperbolic Polynomials with Random Coefficients," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2015, pages 1-7, August.
    • Handle: RePEc:hin:jijmms:261370
    DOI: 10.1155/2015/261370
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    References listed on IDEAS

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    1. Mahanti, Mina Ketan, 2004. "Expected number of real zeros of random hyperbolic polynomial," Statistics & Probability Letters, Elsevier, vol. 70(1), pages 11-18, October.
    2. J. Ernest Wilkins, 2000. "Mean number of real zeros of a random hyperbolic polynomial," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 23, pages 1-8, January.
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