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The problem of directed polymers in a random medium is generalized to include a killing probability. The model is then studied using results of the theory of extreme statistics. These reveal that, in a region of parameters, the thermodynamics of polymers with killing in finite dimensions is similar to that of the mean field solution of directed polymers on a Cayley tree. The implication of these results for the behaviour of directed polymers in high dimensions is also discussed.
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Matteo Marsili (1996) studied this question.
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