A note on random orthogonal polynomials on a compact interval

Abstract

We consider a uniform distribution on the set ${\mathcal{M}}_k$ of moments of order $k\in \mathbb{N}$ corresponding to probability measures on the interval $[0,1]$. To each (random) vector of moments in ${\mathcal{M}}_{2n-1}$ we consider the corresponding uniquely determined monic (random) orthogonal polynomial of degree $n$ and study the asymptotic properties of its roots if $n\to \infty$.

14 pages