Year: 2025
Type: article
Abstract: We study the totally asymmetric simple exclusion process (TASEP) on Z with a general initial condition and a deterministically moving wall in front of the particles. Using colour-position symmetry, we express the one-point distributions in terms of particle positions in a TASEP with step initial condition along a space-like path. Based on this formula, we analyse the large-time asymptotics of the model under various scenarios. For initial conditions other than the step initial condition, we identify a distinct asymptotic behaviour at the boundary of the region influenced by the wall, differing from the observations made in [7, 26]. Furthermore, we demonstrate that product limit distributions are associated with shocks in the macroscopic empirical density. As a special case of our starting formula, we derive a variational expression for the one-point distributions of TASEP with arbitrary initial data. Focusing on non-random initial conditions, such as periodic ones with an arbitrary density, we leverage our analytical tools to characterise the limit distribution within the framework of particle positions.
DOI: 10.1214/25-ejp1367
Author: Sabrina Gernholt
Institution: University of Bonn
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $675
OpenAlex ID: W4411712044