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On the Brownian-directed polymer in a Gaussian random environment. (English) Zbl 1115.60107

Summary: We introduce a model of Brownian polymer in a continuous random environment. The asymptotic behavior of the partition function associated to this polymer measure is studied, and we are able to separate a weak and strong disorder regime under some reasonable assumptions on the spatial covariance of the environment. Some further developments, concerning some concentration inequalities for the partition function, are given for the weak disorder regime.

MSC:

60K37 Processes in random environments
60H07 Stochastic calculus of variations and the Malliavin calculus
82D60 Statistical mechanics of polymers
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