Influence of the initial condition in equilibrium last-passage percolation models

Eric A. Cator (Delft University of Technology)
Leandro P. R. Pimentel (Universidade Federal do Rio de Janeiro)
Marcio W. A. Souza (University of Sao Paulo)

Abstract


In this paper we consider an equilibrium last-passage percolation model on an environment given by a compound two-dimensional Poisson process. We prove an $\mathbb{L}^2$-formula relating the initial measure with the last-passage percolation time. This formula turns out to be a useful tool to analyze the fluctuations of the last-passage times along non-characteristic directions.


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Pages: 1-7

Publication Date: January 30, 2012

DOI: 10.1214/ECP.v17-1727

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