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arxiv: 1307.7769 · v2 · pith:WMRCABTMnew · submitted 2013-07-30 · 🧮 math.PR

Duality between coalescence times and exit points in last-passage percolation models

classification 🧮 math.PR
keywords coalescencetimesdualityexitlast-passagemodelspercolationpoints
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In this paper we prove a duality relation between coalescence times and exit points in last-passage percolation models with exponential weights. As a consequence, we get lower bounds for coalescence times with scaling exponent 3/2, and we relate its distribution with variational problems involving the Brownian motion process and the Airy process.

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