Fluctuation exponents for directed polymers in the intermediate disorder regime. (English) Zbl 1333.60203

Summary: We derive exact fluctuation exponents for a solvable model of one-dimensional directed polymers in random environment in the intermediate scaling regime. This regime corresponds to taking the inverse temperature to zero as the size of the system goes to infinity. The exponents satisfy the KPZ scaling relation and coincide with physical predictions. In the critical case, we recover the fluctuation exponent of the Hopf-Cole solution of the KPZ equation in equilibrium and close to equilibrium.


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