DIFFUSION OF DIRECTED POLYMERS IN A STRONG RANDOM ENVIRONMENT

We consider a system of random walks or directed polymers interacting with an environment which is random in space and time. It was shown by Imbrie and Spencer that in spatial dimensions three or above the beha vior is diffusive if the directed polymer interacts weakly with the en vironment and if the random environment follows the Bernoulli distribu tion. Under the same assumption on the random environment as that of I mbrie and Spencer, we establish that in spatial dimensions four or abo ve the behavior is still diffusive even when the directed polymer inte racts strongly with the environment. More generally, we can prove that , if the random environment is bounded and if the supremum of the supp ort of the distribution has a positive mass, then there is an integer d(o) such that in dimensions higher than d(o) the behavior of the rand om polymer is always diffusive.