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Scaling for a one-dimensional directed polymer with boundary conditions. (English) Zbl 1254.60098

Ann. Probab. 40, No. 1, 19-73 (2012); erratum ibid. 45, No. 3, 2056-2058 (2017).
A directed polymer in a random environment is a model which describes a polymer (that is to say a long chain of molecules) as a random walk path which interacts with a random environment. Here, one considers (and defines) a polymer model with boundaries which are assigned distinct weight distributions, and one derives upper and lower bounds for the model with boundary. One gives detailed results for the fluctuations of a path in the model with boundaries for a polymer with fixed endpoint but without boundaries and for a polymer with free endpoint.

MSC:

60K37 Processes in random environments
60K35 Interacting random processes; statistical mechanics type models; percolation theory
82B41 Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics
82D60 Statistical mechanics of polymers
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