This paper provides information about the asymptotic behavior of a one-dimensional Brownian polymer in random medium represented by a Gaussian field $W$ on ${ \mathbb{ R}}_+\times{ \mathbb{ R}}$ which is white noise in time and function-valued in space. According to the behavior of the spatial covariance of $W$, we give a lower bound on the power growth (wandering exponent) of the polymer when the time parameter goes to infinity: the polymer is proved to be superdiffusive, with a wandering exponent exceeding any $\alpha<3/5$.
Categories: math.PR