Directed last passage site percolation is a kind of optimization
question in a random environment. We will consider a 2-dimensional
model, which can also be thought of as a model for a randomly growing
interface in 2-D, or a queueing model, or a 1-D traffic model (totally
asymmetric simple exclusion process). We will discuss two things.
The first one is a proof of a universality of this model and its
connection to random matrix theory, and the second is, in terms of
the traffic model, a blockage of traffic due to a few slow cars.
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