Abstract
We study the mean survival probability (n) at time n on a random one-dimensional chain with perfect absorbers at 0 and L. The transition probabilities gi at the lattice sites i, are independent identically distributed random variables having the distribution p(gi) = 1 for 0 gi1. We prove the asymptotic inequality, C1(n)n2/(logn)L-3 C2 where C1 and C2 are finite positive constants which depend on the lattice size L, but not on n. We confirm this result by simulations for lattice sizes up to L = 17.
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