Tree polymers in the infinite volume limit at critical strong disorder

Details Tree polymers in the infinite volume limit at critical strong disorder Tree polymers in the infinite volume limit at critical strong disorder

2010-07-12

arxiv.org/abs/1007.1991v3

Mathematics

Probability

Final version

Scientific paper

The a.s. existence of a polymer probability in the infinite volume limit is readily obtained under general conditions of weak disorder from standard theory on multiplicative cascades or branching random walk. However, speculations in the case of strong disorder have been mixed. In this note existence of an infinite volume probability is established at critical strong disorder for which one has convergence in probability. Some calculations in support of a specific formula for the a.s. asymptotic variance of the polymer path under strong disorder are also provided.

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