I am trying to understand the the following paper https://arxiv.org/pdf/1810.10971.pdf, in particular Example 2:

If $ Y \sim N(0,1)$, the standard normal on $\mathbb{R}$, then

$ \begin{align*} \Big( \mathbb{E} \Big[ \frac{1}{m!} Y^{\otimes m }\Big]\Big)_{m \geq 0 } = \exp\Big(\frac{1}{2} e_1 \otimes e_1 \Big) \in \prod_{m \geq 0 } \mathbb{R}^{\otimes m} \end{align*},$

where $e_1$ is the unit basis vector of $\mathbb{R}$ and $\exp$ is defined in the following way:

\begin{align*} \exp &: \prod_{m \geq 0 } V^{\otimes m} \to \prod_{m \geq 0 } V^{\otimes m},\\ exp(s) &:= \sum_{m \geq 0} \frac{s^{\otimes m}}{m!} \end{align*}

What does it mean to take a tensor product of random variables? In particular, what is $\mathbb{E} \Big[ Y^{ \otimes 3 }\Big]$, for example?