LA Probability Forum

UCLA, Math Sciences, Rm 6627

In the colored asymmetric simple exclusion process, one places a particle of "color" -k at each integer site k ∈ \Z. Particles attempt to swap places with an adjacent particle: at rate q ∈ [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.