Shift-Invariance of the Colored TASEP and Finishing Times of the Oriented Swap Process

Abstract

We prove a new shift-invariance property of the colored TASEP. From the shift-invariance of the colored stochastic six-vertex model (proved in Borodin-Gorin-Wheeler or Galashin), one can get a shift-invariance property of the colored TASEP at one time, and our result generalizes this to multiple times. Our proof takes the single-time shift-invariance as an input, and uses analyticity of the probability functions and induction arguments. We apply our shift-invariance to prove a distributional identity between the finishing times of the oriented swap process and the point-to-line passage times in exponential last-passage percolation, which is conjectured by Bisi-Cunden-Gibbons-Romik and Bufetov-Gorin-Romik, and is also equivalent to a purely combinatorial identity related to the Edelman-Greene correspondence. With known results from last-passage percolation, we also get new asymptotic results on the colored TASEP and the finishing times of the oriented swap process.

47 pages, 12 figures. Revised according to referee reports. Adv. Math. to appear

References in corpus (6)

• The oriented swap process
• Shift-invariance for vertex models and polymers
• Interacting particle systems and random walks on Hecke algebras
• Convergence of the Environment Seen from Geodesics in Exponential Last-Passage Percolation
• Sorting networks, staircase Young tableaux and last passage percolation
• The oriented swap process and last passage percolation