Ivan Corwin - Scaling limit of colored ASEP - IPAM at UCLA

May 24, 2024
Recorded 24 May 2024. Ivan Corwin of Columbia University presents "Scaling limit of colored ASEP" at IPAM's Vertex Models: Algebraic and Probabilistic Aspects of Universality Workshop. Abstract: Each site x in Z is initially occupied by a particle of color -x. Across each bond (x,x+1) particles swap places at rate 1 or q 1 depending on whether they are in reverse order (e.g. color 2 then 1) or order (color 1 then 2). This process describes a bijection of Z-- Z which starts maximally in reverse order and randomly drifts towards being ordered. Another name for this model is the "colored asymmetric simple exclusion process". I will explain how to use the Yang-Baxter equation along with techniques involving Gibbs line ensemble to extract the space-time scaling limit of this process, as well as a discrete time analog, the "colored stochastic six vertex model". The limit is described by objects in the Kardar-Parisi-Zhang universality class, namely the Airy sheet, directed landscape and KPZ fixed point. This is joint work with Amol Aggarwal and Milind Hegde. Learn more online at: