Asymmetry in repeated isotropic rotations

@article{Schrder2019AsymmetryIR,
  title={Asymmetry in repeated isotropic rotations},
  author={Malte Schr{\"o}der and Marc Timme},
  journal={Physical Review Research},
  year={2019}
}
Random operators constitute fundamental building blocks of models of complex systems yet are far from fully understood. Here, we explain an asymmetry emerging upon repeating identical isotropic (uniformly random) operations. Specifically, in two dimensions, repeating an isotropic rotation twice maps a given point on the two-dimensional unit sphere (the unit circle) uniformly at random to any point on the unit sphere, reflecting a statistical symmetry as expected. In contrast, in three and… 
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