  A random walk is performed over a disordered media composed of $N$ sites
random and uniformly distributed inside a $d$-dimensional hypercube. The walker
cannot remain in the same site and hops to one of its $n$ neighboring sites
with a transition probability that depends on the distance $D$ between sites
according to a cost function $E(D)$. The stochasticity level is parametrized by
a formal temperature $T$. In the case $T = 0$, the walk is deterministic and
ergodicity is broken: the phase space is divided in a ${\cal O}(N)$ number of
attractor basins of two-cycles that trap the walker. For $d = 1$, analytic
results indicate the existence of a glass transition at $T_1 = 1/2$ as $N \to
\infty$. Below $T_1$, the average trapping time in two-cycles diverges and
out-of-equilibrium behavior appears. Similar glass transitions occur in higher
dimensions choosing a proper cost function. We also present some results for
the statistics of distances for Poisson spatial point processes.
