This article investigates coefficient randomizations of holomorphic functions and the resulting random analytic functions within the framework of mixed norm spaces. Adopting the perspective of the random symbol space $(\mathcal {X})_{\star }=\{f\in H(\mathbb {B}_n): \mathbb {P}(\mathcal {R} f\in \mathcal {X})=1\}$, we first focus on the unit disk $\mathbb {D}$. Specifically, for $q\geq 4$, we identify the conditions under which the random symbol space of the mixed-norm space $H^{p,q,u}(\mathbb {D})$ coincides with $H^{2,q,u}(\mathbb {D})$. Furthermore, we extend our analysis to the higher-dimensional unit ball $\mathbb {B}_n$. We establish sufficient conditions and necessary constraints linking the deterministic membership of a function to the almost sure membership of its randomization in mixed norm spaces. A key finding is the identification of a sharp, dimension-dependent weight loss phenomenon that arises for $n>1$.

Let $f(z)=\sum _{n=0}^{\infty }a_n z^n \in H(\mathbb {D})$ be an analytic function over the unit disk in the complex plane, and let $\mathcal {R} f$ be its randomization:

$$ \begin{align*}(\mathcal{R} f)(z)= \sum_{n=0}^{\infty} a_n X_n z^n \in H(\mathbb{D}),\end{align*} $$

where $(X_n)_{n\ge 0}$ is a standard sequence of independent Bernoulli, Steinhaus, or Gaussian random variables. In this note, we characterize those $f(z) \in H(\mathbb {D})$ such that the zero set of $\mathcal {R} f$ satisfies a Blaschke-type condition almost surely:

$$ \begin{align*}\sum_{n=1}^{\infty}(1-|z_n|)^t<\infty, \quad t>1.\end{align*} $$