Abstract
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.
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References
E. Bolthausen, A note on the diffusion of directed polymers in a random environment,Commun. Math. Phys. 123:529–534 (1989).
L. Breiman,Probability (Addison-Wesley, Reading, Massachusetts, 1968).
J. Z. Imbrie and T. Spencer, Diffusion of directed polymers in a random environment,J. Stat. Phys. 52:609–626 (1988).
M. Krasnoselskii,Positive Solutions of Operator Equations (Noordhoff, Groningen, 1964).
D. Ruelle,Statistical Mechanics-Rigorous Results (Benjamin, 1969).
A. Taylor,Functional Analysis (Wiley, New York, 1958).
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Conlon, J.G., Olsen, P.A. A Brownian motion version of the directed polymer problem. J Stat Phys 84, 415–454 (1996). https://doi.org/10.1007/BF02179650
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DOI: https://doi.org/10.1007/BF02179650