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This paper is about simple random walks on $Z^d$, $d \ge 3$, in a random field of traps, the density of which tends to zero at infinity. We distinguish between the quenched problem (when the traps are fixed) and the annealed problem (when the traps are updated each unit of time). Our goal is not only to find a criterion for zero vs. positive probability of survival, but also to show three differen
