This week

The graphical construction of the asymmetric simple exclusion process (ASEP) provides a coupling to a common iid Poissonian environment of the evolution of any initial data started at any time. I will describe how the scaling limit of this coupled evolution over all initial data and starting times is given in terms of variational problems involving the directed landscape. I will then explain how the Yang-Baxter equation and machinery of Gibbsian line ensembles provides a systematic route to extract this limit, as well as that of any model in Integrable Probability.