Sharp behavior of the free energy for the two-dimensional directed polymer model

Quentin Berger, Shuta Nakajima

We consider the directed polymer model on ${\mathbb{Z}}^d$, in an i.i.d.\ random environment $\ddot{I}‰=(\ddot{I}{‰}_{n,x}{)}_{n\ge 0,x\in {\mathbb{Z}}^d}$, focusing on the critical dimension $d=2$. Our…