Statistics of TASEP with Three Merging Characteristics
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In this paper we consider the totally asymmetric simple exclusion process, with non-random initial condition having three regions of constant densities of particles. From left to right, the densities of the three regions are increasing. Consequently, there are three characteristics which meet, i.e. two shocks merge. We study the particle fluctuations at this merging point and show that they are given by a product of three (properly scaled) GOE Tracy–Widom distribution functions. We work directly in TASEP without relying on the connection to last passage percolation.
KeywordsShock fluctuations Exclusion process KPZ universality class
This work is supported by the Deutsche Forschungsgemeinschaft (German Research Foundation) by the CRC 1060 (Projektnummer 211504053) and Germany’s Excellence Strategy - GZ 2047/1, Projekt ID 390685813.
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