Level Crossings and Turning Points of Random Hyperbolic Polynomials

On the average number of sharp crossings of certain Gaussian random polynomials

Level Crossings of a Random Polynomial with Hyperbolic Elements

This paper provides an asymptotic estimate for the expected number of AMevel crossings of a random hyperbolic polynomial gi cosh x + g2 cosh 2x + ■ ■ ■ + g„ cosh nx , where g¡ (j = 1, 2,..., n) are independent normally distributed random variables with mean zero, variance one and K is any constant independent of x . It is shown that the result for K = 0 remains valid as long as K = K„ = 0{s/n).

Research Article On Zeros of Self-Reciprocal Random Algebraic Polynomials

This paper provides an asymptotic estimate for the expected number of level crossings of a trigonometric polynomial TN (θ)= ∑N−1 j=0 {αN− j cos( j +1/2)θ + βN− j sin( j +1/2)θ}, where αj and βj , j = 0,1,2, . . . ,N − 1, are sequences of independent identically distributed normal standard random variables. This type of random polynomial is produced in the study of random algebraic polynomials w...

Bounds of the Number of Level Crossings of the Random Algebraic Polynomials

-In this paper we have estimate bounds of the number of level crossings of the random algebraic polynomials     n k k k n x t a x f 0 0 ) ( ) 1 , ( where , 1 0 , ) (    t t t ak are dependent random variables assuming real values only and following the normal distribution with mean zero and joint density function      M M s a ' ) 2 / 1 ( exp ) 2 ( / 2 / 1   . There exists an integ...

Twisted Alexander Polynomials of Hyperbolic Knots

We study a twisted Alexander polynomial naturally associated to a hyperbolic knot in an integer homology 3-sphere via a lift of the holonomy representation to SL(2,C). It is an unambiguous symmetric Laurent polynomial whose coefficients lie in the trace field of the knot. It contains information about genus, fibering, and chirality, and moreover is powerful enough to sometimes detect mutation. ...