Deviations of Ergodic Averages for Toral Translations–part Ii: Boxes


We study the Kronicker sequence {nα}n≤N on the torus T where α is uniformly distributed on T. We show that the discrepancy of the number of visits of this sequence to a random box normalized by ln N converges as N → ∞ to a Cauchy distribution. The key ingredient of the proof is a Poisson limit theorem for the Cartan action on the space of d + 1 dimensional… (More)


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