  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.
