Abstract

The KPZ class is a very large set of 1+1 models that are meant to describe random growth interfaces. It is believed that upon scaling, the long time behavior of members in this class is universal and is described by a limiting random object, a Markov process called the KPZ fixed-point. The (one-type) stationary measures for the KPZ fixed-point as well as many models in the KPZ class are known – it is a family of distributions parametrized by some set Iind that depends on the model. For k∈ ℕ the k-type stationary distribution with intensities ρ1,...,ρk ∈ Iind is a coupling of one-type stationary measures of indices ρ1,...,ρk that is stationary with respect to the model dynamics. In this talk we will present recent progress in our understanding of the multi-type stationary measures of the KPZ fixed-point as well as the scaling limit of multi-type stationary measures of two families of models in the KPZ class: metric-like models (e.g. last passage percolation) and particle systems (e.g. exclusion process). Based on joint work with Timo Seppalainen and Evan Sorensen.