Spherical averages in the space of marked lattices

@article{Marklof2016SphericalAI,
  title={Spherical averages in the space of marked lattices},
  author={Jens Marklof and Ilya Vinogradov},
  journal={Geometriae Dedicata},
  year={2016},
  volume={186},
  pages={75-102}
}
A marked lattice is a d-dimensional Euclidean lattice, where each lattice point is assigned a mark via a given random field on $${\mathbb {Z}}^d$$Zd. We prove that, if the field is strongly mixing with a faster-than-logarithmic rate, then for every given lattice and almost every marking, large spheres become equidistributed in the space of marked lattices. A key aspect of our study is that the space of marked lattices is not a homogeneous space, but rather a non-trivial fiber bundle over such a… CONTINUE READING
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