EXACT RESULTS ON SINAIS DIFFUSION

We study the continuum version of Sinai's problem of a random walker i n a random force field in one dimension. A method of stochastic repres entation is used to represent various probability distributions in thi s problem (mean probability density function and first passage time di stributions). This method reproduces already known rigorous results an d also confirms directly some recent results derived using approximati on schemes. We demonstrate clearly, in the Sinai scaling regime, that the disorder dominates the problem and that the thermal distributions tend to zero-one laws.