Limit processes for TASEP with shocks and rarefaction fans

Understand

We consider the totally asymmetric simple exclusion process (TASEP) with two-sided Bernoulli initial condition, i.e., with left density rho_- and right density rho_+.

• We consider the associated height function, whose discrete gradient is given by the particle occurrences.
• Macroscopically one has a deterministic limit shape with a shock or a rarefaction fan depending on the values of rho_{+/-}.
• We characterize the large time scaling limit of the fluctuations as a function of the densities rho_{+/-} and of the different macroscopic regions.