Table of Contents
Journal of Applied Mathematics and Stochastic Analysis
Volume 2006, Article ID 13980, 6 pages
http://dx.doi.org/10.1155/JAMSA/2006/13980

Real zeros of random algebraic polynomials with binomial elements

1Faculty of Mathematics, Shahrood University of Technology, P.O. Box 316-36155, Shahrood, Iran
2Department of Mathematics, University of Ulster, Jordanstown Campus, County Antrim BT37 0QB, United Kingdom

Received 26 August 2005; Revised 26 September 2005; Accepted 26 September 2005

Copyright © 2006 A. Nezakati and K. Farahmand. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. A. P. Aldous and Y. V. Fyodorov, “Real roots of random polynomials: universality close to accumulation points,” Journal of Physics A: Mathematical and General, vol. 37, no. 4, pp. 1231–1239, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. P. Bleher and X. Di, “Correlations between zeros of a random polynomial,” Journal of Statistical Physics, vol. 88, no. 1-2, pp. 269–305, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. P. Bleher and X. Di, “Correlations between zeros of non-Gaussian random polynomials,” International Mathematics Research Notices, vol. 2004, no. 46, pp. 2443–2484, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. E. Bogomolny, O. Bohigas, and P. Leboeuf, “Distribution of roots of random polynomials,” Physical Review Letters, vol. 68, no. 18, pp. 2726–2729, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. E. Bogomolny, O. Bohigas, and P. Leboeuf, “Quantum chaotic dynamics and random polynomials,” Journal of Statistical Physics, vol. 85, no. 5-6, pp. 639–679, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. A. Edelman and E. Kostlan, “How many zeros of a random polynomial are real?,” Bulletin of the American Mathematical Society, vol. 32, no. 1, pp. 1–37, 1995. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. K. Farahmand, Topics in Random Polynomials, vol. 393 of Pitman Research Notes in Mathematics Series, Longman, Harlow, 1998. View at Zentralblatt MATH · View at MathSciNet
  8. K. Farahmand and A. Nezakati, “Algebraic polynomials with non-identical random coefficients,” Proceedings of the American Mathematical Society, vol. 133, no. 1, pp. 275–283, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. I. A. Ibragimov and N. B. Maslova, “On the expected number of real zeros of random polynomials. II. Coefficients with non-zero means,” Theory of Probability and Its Applications, vol. 16, no. 3, pp. 485–493, 1971. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. M. Kac, “On the average number of real roots of a random algebraic equation,” Bulletin of the American Mathematical Society, vol. 49, pp. 314–320, 1943. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. A. Ramponi, “A note on the complex roots of complex random polynomials,” Statistics & Probability Letters, vol. 44, no. 2, pp. 181–187, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. S. O. Rice, “Mathematical analysis of random noise,” The Bell System Technical Journal, vol. 24, pp. 46–156, 1945, reprinted in: Selected Papers on Noise and Stochastic Processes (N. Wax ed.), Dover, New York, 1954, pp. 133–294. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. M. Sambandham, “On a random algebraic equation,” Journal of the Indian Mathematical Society, vol. 41, no. 1-2, pp. 83–97, 1977. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet