The maximum of the two dimensional Gaussian directed polymer in the subcritical regime

Clément Cosco, Shuta Nakajima, Ofer Zeitouni

We study the maximum ${\varphi }_N^{\ast }$ of the partition function of the two dimensional (subcritical) Gaussian directed polymer over an $\sqrt{N}\times \sqrt{N}$ box. We show that $ϕ_N^*/\log…