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We study the sequence alignment problem and its independent version, the discrete Hammersley process with an exploration penalty. We obtain rigorous upper bounds for the number of optimality regions in both models near the soft edge. At zero penalty the independent model becomes an exactly solvable model and we identify cases for which the law of the last passage time converges to a Tracy-Widom law.
We prove a large deviation principle and give an expression for the rate function, for the last passage time in a Bernoulli environment. The model is exactly solvable and its invariant version satisfies a Burke-type property. Finally, we compute expl
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 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
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