The talk has two parts. In the first part we will speak on the modulus of continuity in Poissonian last passage percolation, a model lying in the KPZ universality class. In the second part we speak on the “slow bond” model, where Totally Asymmetric Simple Exclusion Process (TASEP) on $\mathbb{Z}$ (a model which can be thought to simulate a one-way traffic movement) is modified by adding...