  We use Cram\'er-Chernoff type estimates in order to study the
Calder\'on-Zygmund structure of the kernels
$\sum_{I\in\mathcal{D}}a_I(\omega)\psi_I(x)\psi_I(y)$ where $a_I$ are
subgaussian independent random variables and $\{\psi_I: I\in\mathcal{D}\}$ is a
wavelet basis where $\mathcal{D}$ are the dyadic intervals in $\mathbb{R}$. We
consider both, the cases of standard smooth wavelets and the case of the Haar
wavelet.
