# 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},
journal={Mathematische Zeitschrift},
year={2006},
volume={254},
pages={837-870}
}
• Published 31 March 2006
• Mathematics
• Mathematische Zeitschrift
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.
We discuss a large deviation principle of a periodic random walk on a covering graph with its transformation group of polynomial volume growth in view of geometry. As we shall observe, the behavior
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