  We study a detection problem in the following setting: On the one-dimensional
integer lattice, at time zero, place nodes on each site independently with
probability $\rho \in [0,1)$ and let them evolve as a simple symmetric
exclusion process. At time zero, place a target at the origin. The target moves
only at integer times, and can move to any site that is within distance $R$
from its current position. Assume also that the target can predict the future
movement of all nodes. We prove that, for $R$ large enough (depending on the
value of $\rho$) it is possible for the target to avoid detection forever with
positive probability. The proof of this result uses two ingredients of
independent interest. First we establish a renormalisation scheme that can be
used to prove percolation for dependent oriented models under a certain
decoupling condition. This result is general and does not rely on the
specifities of the model. As an application, we prove our main theorem for
different dynamics, such as independent random walks and independent renewal
chains. We also proof existence of oriented percolation for random
interlacements and for its vacant set for large dimensions . The second step of
the proof is a space-time decoupling for the exclusion process.

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