Hall-Littlewood RSK field

Understand

We introduce a randomized Hall-Littlewood RSK algorithm and study its combinatorial and probabilistic properties.

• On the probabilistic side, a new model --- the Hall-Littlewood RSK field --- is introduced.
• Its various degenerations contain known objects (the stochastic six vertex model, the asymmetric simple exclusion process) as well as a variety of new ones.
• We provide formulas for a rich class of observables of these models, extending existing results about Macdonald processes.