Assign to the lattice sizes $z \epsilon \mathbb{Z}^d$ i.i.d. random
2 $d$-dimensional vectors $(\omega(z, z + e))_{|e|=1}$ whose entries take
values in the open unit interval and add up to one. Given a realization
$\omega$ of this environment, let $(X_n)_{n \geq o}$ be a Markov chain on
$\mathbb{Z}^d$ which, when at $z$, moves one step to its neighbor $z + e$
with transition probability $\omega(z, z + e)$. We derive a large deviation
principle for $X_n/n$ by means of a result similar to the shape theorem of
first-passage percolation and related models. This result produces certain
constants that are the analogue of the Lyapounov exponents known from Brownian
motion in Poissonian potential or random walk in random potential. We follow a
strategy similar to Sznitman.
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