Nonstationary Generalized TASEP in KPZ and Jamming Regimes

We study the model of totally asymmetric exclusion process with generalized update, which compared to usual process, has an additional parameter enhancing clustering particles. derive exact multiparticle distributions distances travelled by particles on infinite lattice for two types initial conditions: step and alternating ones. Two different scaling limits formulas are studied. Under first associated Kardar–Parisi–Zhang (KPZ) universality class we prove convergence joint scaled particle positions finite-dimensional universal $$\hbox {Airy}_2$$ {Airy}_1$$ processes. second same position new random processes, describe transition between KPZ regime deterministic aggregation regime, in stick together into a single giant cluster moving as one particle. It is shown that transitional have Airy processes fully correlated Gaussian fluctuations limiting cases. also give heuristic arguments explaining how non-universal constants appearing from asymptotic analysis related properties translationally invariant stationary states system parameters should scale regime.