The $q$-Hahn asymmetric exclusion process

Understand

We introduce new integrable exclusion and zero-range processes on the one-dimensional lattice that generalize the $q$-Hahn TASEP and the $q$-Hahn Boson (zero-range) process introduced in [Pov13] and further studied in [Cor14], by allowing jumps in both directions.

• Owing to a Markov duality, we prove moment formulas for the locations of particles in the exclusion process.
• This leads to a Fredholm determinant formula that characterizes the distribution of the location of any particle.
• We show that the model-dependent constants that arise in the limit theorems predicted by the KPZ scaling theory are recovered by a steepest descent analysis of the Fredholm determinant.