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arXiv · 2010.12312

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

Naotaka Kajino·Kosei Konishi·Makoto Nakashima
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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 $F_q(β)$, $F_a(β)$ and (ii) that $F_a(β)-F_q(β)$ is comparable to $β^{\frac{4}{2-d_{s}}}$ for small inverse temperature $β$.

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Naotaka Kajino, Kosei Konishi, Makoto Nakashima. 2020-10-23. Two-sided bounds on free energy of directed polymers on strongly recurrent graphs. https://arxiv.org/abs/2010.12312

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