Large deviation principle for linear mod 1 transformations

Yong Moo Chung ad Kenichiro Yamamoto

For $0\le \alpha <1$ and $\beta >2$, we consider a linear mod 1 transformation on a unit interval; $x\mapsto \beta x+\alpha$ ($\mathrm{mod}1$), and prove that it satisfies the level-2 large deviation pri…