Large deviation and the tangent cone at infinity of a crystal lattice

@article{Kotani2006LargeDA,
  title={Large deviation and the tangent cone at infinity of a crystal lattice},
  author={M. Kotani and Toshikazu Sunada},
  journal={Mathematische Zeitschrift},
  year={2006},
  volume={254},
  pages={837-870}
}
We discuss a large deviation property of a periodic random walk on a crystal lattice in view of geometry, and relate it to a rational convex polyhedron in the first homology group of a finite graph, which, as we shall observe, has remarkable combinatorial features, and shows up also in the Gromov-Hausdorff limit of a crystal lattice. 
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