Empirical Measures, Geodesic Lengths, and a Variational Formula in First-Passage Percolation Peter J. Giordano Mark Hutchinson

Mark Hutchinson

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Empirical Measures, Geodesic Lengths, and a Variational Formula in First-Passage Percolation Peter J. Giordano Mark HutchinsonThis monograph resolves in a dense class of cases several open problems concerning geodesics in i. i. d. first passage percolation on Zd. Our primary interest is in the empirical measures of edge weights observed along geodesics from 0 to n?, where ? is a fixed unit vector. For various dense families of edge weight distributions, we prove that these empirical measures converge weakly to a deterministic limit as n ? ?, answering a question of Hoffman.