On the local fluctuations of last-passage percolation models

Eric Cator and Leandro P.R. Pimentel

Stochastic Processes and their Applications, 2015, vol. 125, issue 2, 538-551

Abstract: Using the fact that the Airy process describes the limiting fluctuations of the Hammersley last-passage percolation model, we prove that it behaves locally like a Brownian motion. Our method is quite straightforward, and it is based on a certain monotonicity and good control over the equilibrium measures of the Hammersley model (local comparison).

Date: 2015
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DOI: 10.1016/j.spa.2014.08.009

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