We discuss random interpolating sequences in weighted Dirichlet spaces ${{\mathcal{D}}}_\alpha $, $0\leq \alpha \leq 1$, when the radii of the sequence points are fixed a priori and the arguments are uniformly distributed. Although conditions for deterministic interpolation in these spaces depend on capacities, which are very hard to estimate in general, we show that random interpolation is driven by surprisingly simple distribution conditions. As a consequence, we obtain a breakpoint at $\alpha =1/2$ in the behavior of these random interpolating sequences showing more precisely that almost sure interpolating sequences for ${{\mathcal{D}}}_\alpha $ are exactly the almost sure separated sequences when $0\le \alpha <1/2$ (which includes the Hardy space $H^2={{\mathcal{D}}}_0$), and they are exactly the almost sure zero sequences for ${{\mathcal{D}}}_\alpha $ when $1/2 \leq \alpha \le 1$ (which includes the classical Dirichlet space ${{\mathcal{D}}}={{\mathcal{D}}}_1$).

中文翻译：

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Dirichlet 空间中的随机插值序列

我们讨论加权 Dirichlet 空间 ${{\mathcal{D}}}_\alpha $, $0\leq \alpha \leq 1$ 中的随机插值序列，此时序列点的半径是先验固定且参数一致分散式。尽管这些空间中确定性插值的条件取决于容量，通常很难估计，但我们表明随机插值是由非常简单的分布条件驱动的。结果，我们在这些随机插值序列的行为中在 $\alpha =1/2$ 处获得了一个断点，更准确地表明，几乎可以肯定 ${{\mathcal{D}}}_\alpha $ 的插值序列是完全正确的当$0\le \alpha <1/2$（包括哈代空间$H^2={{\mathcal{D}}}_0$）时几乎确定的分离序列，