The second class particle process at shocks. (English) Zbl 1532.60214
Summary: We consider the totally asymmetric simple exclusion process (TASEP) starting with a shock discontinuity at the origin, with asymptotic densities \(\lambda\) to the left of the origin and \(\rho\) to the right of it and \(\lambda < \rho \). We find an exact identity for the distribution of a second class particle starting at the origin. Then we determine the limiting joint distributions of the second class particle. Bypassing the last passage percolation model, we work directly in TASEP, allowing us to extend previous one-point distribution results via a more direct and shorter ansatz.
MSC:
| 60K35 | Interacting random processes; statistical mechanics type models; percolation theory |
| 82C22 | Interacting particle systems in time-dependent statistical mechanics |
| 15B52 | Random matrices (algebraic aspects) |
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