The second class particle process at shocks

Patrik L. Ferrari and Peter Nejjar

Stochastic Processes and their Applications, 2024, vol. 170, issue C

Abstract: We consider the totally asymmetric simple exclusion process (TASEP) starting with a shock discontinuity at the origin, with asymptotic densities λ to the left of the origin and ρ to the right of it and λ<ρ. 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.

Keywords: Asymmetric exclusion process; Shock fluctuations; Second class particle; Scaling limit (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spa.2024.104298

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