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

Abstract

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)

Topics

Figures and Tables

Sorry, we couldn't extract any figures or tables for this paper.

Slides referencing similar topics