Determinantal Expressions in Multi-Species TASEP
Probability
2020-12-17 v2
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.
Cite
@article{arxiv.2007.02913,
title = {Determinantal Expressions in Multi-Species TASEP},
author = {Jeffrey Kuan},
journal= {arXiv preprint arXiv:2007.02913},
year = {2020}
}