Last passage percolation with a defect line and the solution of the slow bond problem
We address the question of how a localized microscopic defect, especially if it is small with
respect to certain dynamic parameters, affects the macroscopic behavior of a system. In
particular we consider two classical exactly solvable models: Ulam's problem of the maximal
increasing sequence and the totally asymmetric simple exclusion process. For the first
model, using its representation as a Poissonian version of directed last passage percolation
on $\mathbb R^ 2$, we introduce the defect by placing a positive density of extra points …
respect to certain dynamic parameters, affects the macroscopic behavior of a system. In
particular we consider two classical exactly solvable models: Ulam's problem of the maximal
increasing sequence and the totally asymmetric simple exclusion process. For the first
model, using its representation as a Poissonian version of directed last passage percolation
on $\mathbb R^ 2$, we introduce the defect by placing a positive density of extra points …
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