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

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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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Correspondence to Motoko Kotani.

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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

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