Rate function under scalar clipping
= Rate function under scalar clipping
{title2=$K(a)=\inf_{x\le a}I(x),\quad K(b)=\inf_{x\ge b}I(x)$}
For $a<b$, the <contraction principle for large deviations> under <scalar clipping> gives $K(z)=I(z)$ in $(a,b)$, the displayed endpoint costs, and infinite cost outside $[a,b]$. The endpoint costs can differ from $I(a)$ and $I(b)$ because clipping collects a whole input tail into a single output atom.