SPECIAL MIT Probability Seminar
Monday, September 19, 2022 at 3:00pm to 4:30pm
Building 2, 2-132
182 MEMORIAL DR, Cambridge, MA 02139
Speaker: Matteo Mucciconi (University of Warwick)
Title: A bijective approach to solvable KPZ models.
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.
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