First-passage percolation (FPP) is a classical probabilistic model in which random weights are assigned to the edges of a lattice and one studies the minimal passage time between two points. It provides a mathematical description of phenomena such as fluid flow through a random medium and the spread of an infection. Through the geometry of passage times and the associated geodesics, it also serves as a fundamental model in random geometry.

In recent years, the behavior of fluctuations of passage times and the corresponding tail probabilities has attracted considerable attention because of its connection with the scaling behavior observed in the Kardar–Parisi–Zhang (KPZ) universality class. In this talk, I will review known results on fluctuations of passage times and on the geometry of geodesics in FPP, and then present some recent progress on tail estimates. I will also discuss open problems concerning the relationship with the KPZ equation.

16:15 - Tea