# Convergence of the Environment Seen from Geodesics in Exponential Last-Passage Percolation

@inproceedings{Martin2021ConvergenceOT, title={Convergence of the Environment Seen from Geodesics in Exponential Last-Passage Percolation}, author={James B. Martin and Allan Sly and Lingfu Zhang}, year={2021} }

A well-known question in the planar first-passage percolation model concerns the convergence of the empirical distribution along geodesics. We demonstrate this convergence for an explicit model, directed last-passage percolation on Z with i.i.d. exponential weights, and provide explicit formulae for the limiting distributions, which depend on the asymptotic direction. For example, for geodesics in the direction of the diagonal, the limiting weight distribution has density (1/4+x/2+x/8)e, and so… Expand

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