TASEP hydrodynamics using microscopic characteristics

Abstract

The convergence of the totally asymmetric simple exclusion process to the solution of the Burgers equation is a classical result. In his seminal 1981 paper, Herman Rost proved the convergence of the density fields and local equilibrium when the limiting solution of the equation is a rarefaction fan. An important tool of his proof is the subadditive ergodic theorem. We prove his results by showing how second class particles transport the rarefaction-fan solution, as characteristics do for the Burgers equation, avoiding subadditivity. In the way we show laws of large numbers for tagged particles, fluxes and second class particles, and simplify existing proofs in the shock cases. The presentation is self contained.

20 pages, 13 figures. This version is accepted for publication in Probability Surveys, February 20 2018

References in corpus (4)

• Competition interfaces and second class particles
• The motion of a second class particle for the tasep starting from a decreasing shock profile
• A phase transition for competition interfaces
• Euler hydrodynamics of one-dimensional attractive particle systems

Cited by in corpus (7)

• KPZ statistics of second class particles in ASEP via mixing
• Convergence of the Environment Seen from Geodesics in Exponential Last-Passage Percolation
• KPZ fluctuations in finite volume
• Fluctuations for stationary $q$-TASEP
• Nonstationary generalized TASEP in KPZ and jamming regimes
• Mapping TASEP back in time
• Scaling limit of soliton lengths in a multicolor box-ball system