Real zeros of random algebraic polynomials
HTML articles powered by AMS MathViewer
- by K. Farahmand PDF
- Proc. Amer. Math. Soc. 113 (1991), 1077-1084 Request permission
Abstract:
There are many known asymptotic estimates of the expected number of real zeros of algebraic polynomials with independent random coefficients of equal means. The present paper considers the case when the means of the coefficients are not all necessarily equal. The expected number of crossings of two algebraic polynomials with unequal degree flows from the results.References
- Harald Cramér and M. R. Leadbetter, Stationary and related stochastic processes. Sample function properties and their applications, John Wiley & Sons, Inc., New York-London-Sydney, 1967. MR 0217860
- Kambiz Farahmand, On the average number of real roots of a random algebraic equation, Ann. Probab. 14 (1986), no. 2, 702–709. MR 832032
- K. Farahmand, The average number of level crossings of a random algebraic polynomial, Stochastic Anal. Appl. 6 (1988), no. 3, 247–272. MR 949678, DOI 10.1080/07362998808809147 I. A. Ibragimov and N. B. Maslova, On the expected number of real zeros of random polynomials. I. Coefficients with zero means, Theory Probab. Appl. 16 (1971), 228-248. —, On the expected number of real zeros of random polynomials. II. Coefficients with non-zero means, Theory Probab. Appl. 16 (1971), 485-493.
- M. Kac, On the average number of real roots of a random algebraic equation, Bull. Amer. Math. Soc. 49 (1943), 314–320. MR 7812, DOI 10.1090/S0002-9904-1943-07912-8
- M. Kac, On the average number of real roots of a random algebraic equation. II, Proc. London Math. Soc. (2) 50 (1949), 390–408. MR 30713, DOI 10.1112/plms/s2-50.5.390 J. E. Littlewood and A. C. Offord, On the number of real roots of a random algebraic equation, Proc. Cambridge Philos. Soc. 35 (1939), 133-148.
- S. O. Rice, Mathematical analysis of random noise, Bell System Tech. J. 24 (1945), 46–156. MR 11918, DOI 10.1002/j.1538-7305.1945.tb00453.x
Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 113 (1991), 1077-1084
- MSC: Primary 60G99
- DOI: https://doi.org/10.1090/S0002-9939-1991-1077787-5
- MathSciNet review: 1077787