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Majorizing multiplicative cascades for directed polymers in random media. (English) Zbl 1105.60074

Summary: We give upper bounds for the free energy of discrete directed polymers in random media. The bounds are given by the so-called generalized multiplicative cascades from the statistical theory of turbulence. For the polymer model, we derive that the quenched free energy is different from the annealed one in dimension 1, for any finite temperature and general environment. This implies localization of the polymer.

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory