Description:

Title: Classification of the limit shape in 1+1-dimensional first passage percolation

Abstract: First passage percolation is a straightforward model that defines a random graph distance by putting independent and identically distributed weights on each edge. Although it is believed to lie in the very well-studied KPZ universality class, elementary properties remain unproven. For example, while Cox and Durrett proved in 1981 that the random distance converges to a deterministic limit shape, until this day, it is almost completely open how this shape looks like for any non-constant probability distribution. 

It is thus natural to look at simplified versions of FPP first. I will present a version of this model on the two-dimensional integer lattice where horizontal edge weights remain random but vertical edge weights are constant. The main result is an exact criteria when the limit shape has a flat edge in the vertical direction, which we do not yet have for the standard model. Moreover, I will present a conceptual relation between the differentiability of the limit shape and the local geometry of the geodesics.