Two-sided bounds on free energy of directed polymers on strongly recurrent graphs

Abstract

We study the directed polymers in random environment on an infinite graph $G=(V,E)$ on which the underlying random walk satisfies sub-Gaussian heat kernel bounds with spectral dimension $d_s$ strictly less than two. Our goal in this paper is to show (i) the existence and the coincidence of the quenched and the annealed free energy $F_q(\beta )$, $F_a(\beta )$ and (ii) that $F_a(\beta )-F_q(\beta )$ is comparable to ${\beta }^{\frac{4}{2-d_s}}$ for small inverse temperature $\beta$.

References in corpus (2)

• Fractional moment bounds and disorder relevance for pinning models
• Exponential inequalities for martingales and asymptotic properties of the free energy of directed polymers in random environment