The optimal sub-Gaussian normalisation for randomised monotone functions

Thomas Anton, Rabee Tourky

Let $\mathcal{M}$ denote the class of randomised monotone functions on $\mathbb{R}$ with values in $[0,1]$, and let $U_{\mathcal{M}}:{\mathbb{R}}_{+}\to {\mathbb{R}}_{+}$ be the mini…