Asymptotics of dynamic ASEP using duality

Using a recently developed method for proving asymptotics via orthogonal polynomial duality arXiv:2305.17602, we prove that the dynamic ASEP introduced in arXiv:1701.05239 has asymptotics which are either distributed as the Tracy–Widom $F_2,$ or are almost surely bounded. Using a different duality, we also provide contour integrals formulas for multi–species ASEP, which generalize results for the single–species ASEP.