Boundedness and concentration of random singular integrals defined by wavelet summability kernels

We use Cramér-Chernoff type estimates in order to study the Calderón-Zygmund structure of the kernels $\sum_{I\in\mathcal{D}}a_I(ω)ψ_I(x)ψ_I(y)$ where $a_I$ are subgaussian independent random variables and $\{ψ_I: I\in\mathcal{D}\}$ 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.

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