A note on random orthogonal polynomials on a compact interval

Details A note on random orthogonal polynomials on a compact interval A note on random orthogonal polynomials on a compact interval

2008-09-29

arxiv.org/abs/0809.4936v1

Mathematics

Probability

14 pages

Scientific paper

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 $n \to \infty$.

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