A Brownian Motion Version of the Directed Polymer Problem
نویسندگان
چکیده
Consider a Brownian particle in three dimensions in a random environment. The environment is determined by a potential random in space and time. It is shown that at small noise the large-time behavior of the particle is diffusive. The diffusion constant depends on the environment. This work generalizes previous results for random walk in a random environment. In these results the diffusion constant does not depend on the environment.
منابع مشابه
Directed polymers and the quantum Toda lattice
We give a characterization of the law of the partition function of a Brownian directed polymer model in terms of the eigenfunctions of the quantum Toda lattice. This is obtained via a multidimensional generalization of theorem of Matsumoto and Yor concerning exponential functionals of Brownian motion. Mathematics Subject Classification (2000): 15A52, 37K10, 60J65, 82D60.
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تاریخ انتشار 2005