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

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