Joint moments of multi-species $q$-Boson.
1st October 2021, 3:30 pm – 4:30 pm
Fry Building, 2.04 (also on Zoom)
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 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.