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Influence of spatial correlation for directed polymers. (English) Zbl 1208.82084

Summary: We study a model of a Brownian polymer in \(\mathbb R_+\times \mathbb R^d\), introduced by C. Rovira and S. Tindel [J. Funct. Anal. 222, No. 1, 178–201 (2005; Zbl 1115.60107)]. Our investigation focuses mainly on the effect of strong spatial correlation in the environment in that model in terms of free energy, fluctuation exponent and volume exponent. In particular, we prove that under some assumptions, very strong disorder and superdiffusivity hold at all temperatures when \(d\geq 3\) and provide a novel approach to Petermann’s superdiffusivity result in dimension one [Superdiffusivity of directed polymers in random environment, Ph.D. thesis (2000)]. We also derive results for a Brownian model of pinning in a nonrandom potential with power-law decay at infinity.

MSC:

82D60 Statistical mechanics of polymers
60K37 Processes in random environments
60K35 Interacting random processes; statistical mechanics type models; percolation theory

Citations:

Zbl 1115.60107
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References:

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