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Last passage percolation and random matrix theory

4:00 pm Thursday, October 13, 2011
Jinho Baik (University of Michigan)

Imagine that to each lattice site of the 2-dimensional integer lattice, there is a random variable, representing the amount of time one needs to spend to pass through the site. The time one travels from one site to another site through a specific path is the sum of the random variables on the lattice sites in the path. The last passage time from (1,1) to (M,N) is defined as the maximal time it takes to travel from (1,1) to (M,N) among all possible up/right paths. In 2000, Johansson showed that for certain specific random variables, this problem is related to random matrix theory. This is achieved by a combinatorial analysis and is related to a enumeration problem of certain non-intersecting paths. We will survey some of the results on this problem and recent progresses.

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