Abstract
Let x↦x+α be a rotation on the circle and let φ be a step function. Denote by φn(x) the ergodic sums ∑j=0n−1φ(x+jα). For α in a class containing the rotations with bounded partial quotients and under a Diophantine condition on the discontinuities of φ, we show that φn/‖φn‖2 is asymptotically Gaussian for n in a set of density 1.
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