  We consider the nonabelian sandpile model defined on directed trees by Ayyer,
Schilling, Steinberg and Thi\'ery (Commun. Math. Phys, 2013) and restrict it to
the special case of a one-dimensional lattice of $n$ sites which has open
boundaries and disordered hopping rates. We focus on the joint distribution of
the integrated currents across each bond simultaneously, and calculate its
cumulant generating function exactly. Surprisingly, the process conditioned on
seeing specified currents across each bond turns out to be a renormalised
version of the same process. We also remark on a duality property of the large
deviation function. Lastly, all eigenvalues and both Perron eigenvectors of the
tilted generator are determined.
