By Jian DING, The University of Chicago

I will discuss first passage percolation problems in two-dimensional lattice where the vertex weight is given by exponentiating log-correlated Gaussian fields. I will present some recent progress on the exponent for the weight of the geodesic including an upper bound as well
as a non-universality result.

This is based on joint works with Subhajit Goswami and Fuxi Zhang.