Rademacher large-deviation rate function
= Rademacher large-deviation rate function
For a uniform random sign $X\in\{-1,1\}$, $\psi(\lambda)=\log\cosh\lambda$ and
$$
\psi^*(x)
=\frac{(1+x)\log(1+x)+(1-x)\log(1-x)}2
$$
for $|x|\leq1$, with value $+\infty$ outside that interval.