Journal
GEOMETRIAE DEDICATA
Volume 186, Issue 1, Pages 75-102Publisher
SPRINGER
DOI: 10.1007/s10711-016-0180-2
Keywords
Equidistribution; Random process; Homogeneous dynamics; Measure rigidity; Lorentz gas
Categories
Funding
- European Research Council under the European Union [291147]
- European Research Council (ERC) [291147] Funding Source: European Research Council (ERC)
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A marked lattice is a d-dimensional Euclidean lattice, where each lattice point is assigned a mark via a given random field on . 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 space. As an application, we prove that the free path length in a crystal with random defects has a limiting distribution in the Boltzmann-Grad limit.
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