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These lecture notes are written as reference material for the Advanced Course Hydrodynamical Methods in Last Passage Percolation Models, given at the 28th Coloquio Brasileiro de Matematica at IMPA, Rio de Janeiro, July 2011.
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 formul
In this paper we study stationary last passage percolation (LPP) in half-space geometry. We determine the limiting distribution of the last passage time in a critical window close to the origin. The result is a new two-parameter family of distributio
We consider the geodesic of the directed last passage percolation with iid exponential weights. We find the explicit one point distribution of the geodesic location joint with the last passage times, and its limit when the size goes to infinity.
We study first-passage percolation where edges in the left and right half-planes are assigned values according to different distributions. We show that the asymptotic growth of the resulting inhomogeneous first-passage process obeys a shape theorem,
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 $mathbb{Z}^2$ with