Limiting Distributions for Last Passage Percolation

At each site (i,j) in a 2-dimensional lattice, we attach an identically distributed, independent random variable. We regard, for example, the random variable at each site as the time required to pass through that site. Then the interest is in the last passage time to go from the site (1,1) to the site (M,N) along directed paths, as M, N tend to infinity. This last passage percolation problem has applications to random growth models, queueing theory and interacting particle systems. In recent years, the limiting distribution of the last passage time, after suitable centering and scaling, has been found for a few special cases of random variables. We also discuss the symmetrized versions of last passage percolation models.