Matteo Mucciconi: A bijective approach to solvable KPZ models

Abstract

Explicit solutions of random growth models in the KPZ universality class have attracted, in the last two decades, significant attention in Mathematical Physics. A common approach to the problem, explored in the last 15 years, leverages remarkable relations between the KPZ equation and quantum integrable systems.   Here, I will introduce a new approach to the solutions of KPZ models, based on a bijection discovered by Imamura, Sasamoto and myself last year. This is a generalization of the celebrated Robinson-Schensted-Knuth correspondence relating at once 1) solvable growth models, 2) determinantal point processes of free fermionic origin and 3) models of Last Passage Percolation on a cylinder.   I will enumerate some of the early applications of this new approach and I will give an overview of the technical tools needed, that include Kashiwara's crystals or the inverse scattering method for solitonic systems.