  The so-called 'Level 2.5' general result for the large deviations of the
joint probability of the density and of the currents for Markov Jump processes
is applied to the case of $N$ independent particles on a ring with random
transition rates. We first focus on the Directed Trap model, where the
contractions needed to obtain the large deviations properties of the density
alone and of the current alone can be explicitly written in each disordered
sample, and where the deformed Markov operator needed to evaluate the
generating function of the current can be also explicitly analyzed via its
highest eigenvalue and the corresponding left and right eigenvectors. We then
turn to the non-directed model, where the tails for large currents $ j \to \pm
\infty$ of the rate function for the current alone can still be studied
explicitly, either via contraction or via the deformed Markov operator method.
We mention the differences with the large deviations properties of the
Fokker-Planck dynamics on disordered rings.
