Ida Wolf: Last Passage Percolation on a Torus

Abstract: We consider the problem of Poissonian last passage percolation on a torus. Given a torus of area n equipped with a Poisson point process, we are interested in the maximal number of points τn that can be collected by an oriented path on this torus. We study the asymptotic behavior of τn when the number of points on the torus goes to infinity, and we derive upper and lower bounds on the expected value of τn.