Discrete time q-TASEPs

Understand

We introduce two new exactly solvable (stochastic) interacting particle systems which are discrete time versions of q-TASEP.

• We call these geometric and Bernoulli discrete time q-TASEP.
• We obtain concise formulas for expectations of a large enough class of observables of the systems to completely characterize their fixed time distributions when started from step initial condition.
• We then extract Fredholm determinant formulas for the marginal distribution of the location of any given particle.