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Empirical measures, geodesic lengths, and a variational formula in first-passage percolation

Probability Seminar
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Thursday, October 29, 2020
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3:15 pm - 4:15 pm
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Erik Bates
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Probability Seminar

We consider the standard first-passage percolation model on Z^d, in which each edge is assigned an i.i.d. nonnegative weight, and the passage time between any two points is the smallest total weight of a nearest-neighbor path between them. Our primary interest is in the empirical measures of edge-weights observed along geodesics from 0 to ne_1. For various dense families of edge-weight distributions, we prove that these measures converge weakly to a deterministic limit as n tends to infinity. The key tool is a new variational formula for the time constant. In this talk, I will derive this formula and discuss its implications for the convergence of both empirical measures and lengths of geodesics.

Contact Rick Durrett for zoom link.

Contact: Rick Durrett