Random Blaschke products.

Let $\{\theta\sb{n}(\omega)\}$ be a sequence of independent random variables uniformly distributed on (0,2$\pi$), and let $z\sb{n}(\omega) + r\sb{n}e\sp{i\theta n(\omega)}$ for a fixed but arbitrary sequence of radii $r\sb{n}$ satisfying the Blaschke condition $\Sigma(1 - r\sb{n}) < \infty.$ We show that the random Blaschke product with zeros $z\sb{n}(\omega)$ is almost surely not in the little Bloch space, and we describe necessary conditions and sufficient conditions on the radii $r\sb{n}$ so that $\{z\sb{n}(\omega)\}$ is almost surely an interpolating sequence.PhDMathematicsPure SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/128357/2/9001612.pd