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

Abstract

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 $N\to \infty$.

Cited by in corpus (3)

• The intermediate disorder regime for directed polymers in dimension $1+1$
• Central limit theorems for the (2+1)-dimensional directed polymer in the weak disorder limit
• Another look into the Wong-Zakai Theorem for Stochastic Heat Equation