2021/07/13 by Lingfu Zhang, Zhang, Lingfu
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Random Matrices and Applications #Representation Theory (math.RT) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2107.06350
openalex publication_date 2021/07/13 · openalex created_date 2021/07/19 · openalex updated_date 2026/07/28
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.