## Random sequences interpolating with probability one.(English)Zbl 0831.30020

For a sequence $$\{r_n\}_{n \geq 0}$$ of points in $$(0,1)$$ the author considers the question of whether the sequence $$\{r_n e^{i \theta_n}\}_{n \geq 0}$$ of points of the unit disk is interpolating for $$H^\infty$$ for almost all choices of $$\theta_n$$. The main result shows that the sequence $$\{r_n e^{i \theta_n}\}$$ is interpolating with probability 1 if $$\sum_{k \geq 0} 2^{-k} N_k^2 < \infty$$ and is interpolating with probability 0 if $$\sum_{k \geq 0} 2^{-k} N_k^2 = \infty$$, where $$N_k$$ is the number of terms of $$\{r_n\}_{n \geq 0}$$ in $$[1 - 2^{- k}, 1 - 2^{- k - 1})$$.

### MSC:

 30D50 Blaschke products, etc. (MSC2000) 30B20 Random power series in one complex variable

### Keywords:

interpolating sequence
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