Survival probability of random walks leaping over traps

We consider one-dimensional discrete-time random walks (RWs) in the presence of finite size traps length $\ell$ over which RWs can jump. study survival probability such when are periodically distributed and separated by a distance $L$. obtain exact results for mean first-passage time special case double-sided exponential jump distribution. While typically survive longer than if they could not leap traps, their still decreases exponentially with number steps. The decay rate depends non-trivial way on trap exhibits an interesting regime $\ell\rightarrow 0$ as it tends to ratio $\ell/L$, is reminiscent strongly chaotic deterministic systems. generalize our model continuous-time RWs, where we introduce power-law waiting before each In this case, find that decays algebraically exponent independent length. Finally, derive diffusive limit show that, depending chosen scaling, either diffusion uniform absorption, or point absorbers.