The scaling limit of the colored asymmetric simple exclusion process
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 limits 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.