Zi Sheng Feng

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 $β= o(N^{-1/4})$ in d=1 and $β=o((\log N)^{-1/2})$ in $d=2$ as $N\rightarrow \infty$.