The statistical distribution of the zeros of random paraorthogonal polynomials on the unit circle Original Research Article

Φk+1(z)=zΦk(z)-α¯kΦk*(z),k⩾0,Φ0=1,We take image i.i.d. random variables distributed uniformly in a disk of radius image and image another random variable independent of the previous ones and distributed uniformly on the unit circle. For any image we will consider the random paraorthogonal polynomial image. The zeros of image are image random points on the unit circle. We prove that for any image the distribution of the zeros of image in intervals of size image near image is the same as the distribution of image independent random points uniformly distributed on the unit circle (i.e., Poisson). This means that, for large image, there is no local correlation between the zeros of the considered random paraorthogonal polynomials.