In the colored asymmetric simple exclusion process, one places a particle of "color" \$-k\$ at each integer site \$k \in \mathbb Z\$. Particles attempt to swap places with an adjacent particle: at rate \$q\in[0,1)\$ if they are initially ordered (e.g., 1 then 2) and at rate 1 if ordered in reverse (e.g., 2 then 1); thus the particles tend to get more ordered over time. We will discuss the scaling limit of this process, which lies in the Kardar-Parisi-Zhang universality class. It is given by the directed landscape, which was first constructed in 2018 by Dauvergne-Ortmann-Virág as a limit in a very different setting - of fluctuations of a model of a random directed metric. The Yang-Baxter equation and line ensembles (collections of random non-intersecting curves) with certain Gibbs or spatial Markov properties will play fundamental roles in our discussion.
This is based on joint work with Amol Aggarwal and Ivan Corwin.