This paper states a law of large numbers for a random walk in a random iid environment on $Z^d$, where the environment follows some Dirichlet distribution. Moreover, we give explicit bounds for the asymptotic velocity of the process and also an asymptotic expansion of this velocity at low disorder.
"Random Walks in a Dirichlet Environment." Electron. J. Probab. 11 802 - 816, 2006. https://doi.org/10.1214/EJP.v11-350