Exponential decay rate of survival probability in a disastrous random environment
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We study the exponential decay rate of the survival probability up to time t>0 of a random walker moving in Zopf;d in a temporally and spatially fluctuating random environment. When the random walker has a speed parameter κ>0, we investigate the influence of κ on the exponential decay rate λ(d,κ). In particular we prove that for any fixed d≥1, λ(d,κ) behaves like as logκ as κ↘0.
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