Diffusivity of Rescaled Random Polymer in Random Environment in dimensions 1 and 2

Zi Sheng Feng

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 $d=2$…