Zeros of Random Orthogonal Polynomials on the Unit Circle

@inproceedings{Stoiciu2005ZerosOR,
  title={Zeros of Random Orthogonal Polynomials on the Unit Circle},
  author={Mihai Stoiciu},
  year={2005}
}
We consider polynomials on the unit circle defined by the recurrence relation Φk+1(z) = zΦk(z)− αkΦk(z) k ≥ 0, Φ0 = 1 For each n we take α0, α1, . . . , αn−2 to be independent identically distributed random variables uniformly distributed in a disk of radius r < 1 and αn−1 to be another random variable independent of the previous ones and distributed uniformly on the unit circle. The previous recurrence relation gives a sequence of random paraorthogonal polynomials {Φn}n≥0. For any n, the zeros… CONTINUE READING