Determinantal Expressions in Multi-Species TASEP

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.

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Cited by in corpus (3)

• Exact Formulas of the Transition Probabilities of the Multi-Species Asymmetric Simple Exclusion Process
• Transition probability and total crossing events in the multi-species asymmetric exclusion process
• Simplified Forms of the Transition Probabilities of the Two-Species ASEP with Some Initial Orders of Particles