Diffuse Behaviour of Ergodic Sums Over Rotations

Jean-Pierre Conze, Stefano Isola, Stéphane Le Borgne

For a rotation by an irrational $\alpha$ on the circle and a BV function $\phi$, we study the variance of the ergodic sums $S_L\phi (x):={\sum }_{j=0}^{L-1}\phi (x+j\alpha )$. When $\alpha$ is not of…