Wednesday, July 28, 2021 2:00 PM
Jeffrey Kuan

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Zoom ID: 912 7469 3500
Password: 3628800 (= 10!).

Abstract: The Airy_2 process is a universal distribution which describes fluctuations in models in the Kardar--Parisi--Zhang (KPZ) universality class, such as the asymmetric simple exclusion process (ASEP) and the Gaussian Unitary Ensemble (GUE). Despite its ubiquity, there are no proven results for analogous fluctuations of multi--species models. Here, we will discuss one model in the KPZ universality class, the $q$--Boson. We will show that the joint multi--point fluctuations of the single--species $q$--Boson match the single--point fluctuations of the multi--species $q$--Boson. Therefore the single--point fluctuations of multi--species models in the KPZ class ought to be the Airy_2 process. The proof utilizes the underlying algebraic structure of the multi--species $q$--Boson, namely the quantum group symmetry and Coxeter group actions.