Diffusivity of Rescaled Random Polymer in Random Environment in   dimensions 1 and 2
  We show random polymer is diffusive in dimensions 1 and 2 in probability in an intermediate scaling regime. The scale is $\beta= o(N^{-1/4})$ in d=1 and $\beta=o((\log N)^{-1/2})$ in $d=2$ as $N\rightarrow \infty$. 
Zi Sheng Feng
math.PR