On the CLT for rotations and BV functions

Jean-Pierre Conze, Stéphane Le Borgne

Let $x\mapsto x+\alpha$ be a rotation on the circle and let $\phi$ be a step function. We denote by $\phi \_n(x)$ the corresponding ergodic sums $\sum \_{j=0}^{n-1}\phi (x+j\alpha )$. Under an assum…