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

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 $LL^2$-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.