Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 16 (2020), 133, 6 pages      arXiv:2007.02913      https://doi.org/10.3842/SIGMA.2020.133

Determinantal Expressions in Multi-Species TASEP

Jeffrey Kuan
Texas A&M University, Department of Mathematics, Mailstop 3368, College Station, TX 77843-3368, USA

Received July 14, 2020, in final form December 03, 2020; Published online December 11, 2020

Abstract
Consider an inhomogeneous multi-species TASEP with drift to the left, and define a height function which equals the maximum species number to the left of a lattice site. For each fixed time, the multi-point distributions of these height functions have a determinantal structure. In the homogeneous case and for certain initial conditions, the fluctuations of the height function converge to Gaussian random variables in the large-time limit. The proof utilizes a coupling between the multi-species TASEP and a coalescing random walk, and previously known results for coalescing random walks.

Key words: determinantal; multi-species; TASEP; coalescing.

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