Weak disorder for low dimensional polymers: The model of stable laws

Details Weak disorder for low dimensional polymers: The model of stable laws Weak disorder for low dimensional polymers: The model of stable laws

2006-03-16

arxiv.org/abs/math/0603390v1

Mathematics

Probability

Scientific paper

In this paper, we consider directed polymers in random environment with long range jumps in discrete space and time. We extend to this case some techniques, results and classifications known in the usual short range case. However, some properties are drastically different when the underlying random walk belongs to the domain of attraction of an $\a$-stable law. For instance, we construct natural examples of directed polymers in random environment which experience weak disorder in low dimension.

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