The Linear Algebra of the Last Passage Percolation Model

We study the linear algebra of the last passage percolation model. In this model, we want to find the statistics of maximal paths through a randomly weighted grid. Specifically we focus on bases of the set of path lengths made from paths. The maximum path length is a deterministic function of a much smaller subset of random path lengths, yet the asymptotic behavior of the two is fundamentally different. We investigate this phenomena in depth. This paper is based on research done in collaboration with Dr. Tom Alberts and Daniel Lee. ii