Abstract
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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To the memory of our late friend Robert Brooks
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Kotani, M., Sunada, T. Large deviation and the tangent cone at infinity of a crystal lattice. Math. Z. 254, 837–870 (2006). https://doi.org/10.1007/s00209-006-0951-9
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DOI: https://doi.org/10.1007/s00209-006-0951-9