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We address the question of how a localized microscopic defect, especially ifit is small with respect to certain dynamic parameters, affects the macroscopicbehavior of a system. In particular we consider two classical exactly solvablemodels: Ulam's problem of the maximal increasing sequence and the totallyasymmetric simple exclusion process. For the first model, using itsrepresentation as a Poissonian version of directed last passage percolation on$\mathbb R^2$, we introduce the defect by placing a positive density of extrapoints along the diagonal line. For the latter, the defect is produced bydecreasing the jump rate of each particle when it crosses the origin.  The powerful algebraic tools for studying these processes break down in theperturbed versions of the models. Taking a more geometric approach we show thatin both cases the presence of an arbitrarily small defect affects themacroscopic behavior of the system: in Ulam's problem the time constantincreases, and for the exclusion process the flux of particles decreases. This,in particular, settles the longstanding Slow Bond Problem.

Last Passage Percolation with a Defect Line and the Solution of the Slow Bond Problem