Level Crossings of a Class of Random Algebraic Polynomial

Author : Dipty Rani Dhal and Dr. P. K. Mishra

Abstract                                                                           

We know the expected number of times that a polynomial of degree n with independent normally distributed random real coefficients asymptotically crosses the line mx, when m is any real value such that (m²/n)→0 as n→∞. The present paper shows that for m>exp (nf), where f is any function of n such that f(n)→∞, this expected number of crossings reduces to only one.

1991 Mathematics subject classification (Amer. Math. Soc.): 60 B 99.

Keywords and phrases: Level crossings, Trigonometric functions Independent, identically distributed random variables, random algebraic polynomial, random algebraic equation, real roots, domain of attraction of the normal law, slowly varying function.