This paper provides information about the asymptotic behavior of a one-dimensional Brownian polymer in random medium represented by a Gaussian field W on ℝ+×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 α<3/5.
"Superdiffusivity for a Brownian polymer in a continuous Gaussian environment." Ann. Probab. 36 (5) 1642 - 1675, September 2008. https://doi.org/10.1214/07-AOP363