Determinantal Expressions in Multi-Species TASEP

Symmetry Integrability and Geometry-Methods and Applications

article

Jeffrey Kuan¹ 

[1] Texas A&M University, Department of Mathematics, College Station

关键词: determinantal;    multi-species;    TASEP;    coalescing 2020 Mathematics Subject Classification 60J27;   

DOI  :  10.3842/SIGMA.2020.133

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown