论文标题
强烈复发图上有向聚合物的自由能的两侧边界
Two-sided bounds on free energy of directed polymers on strongly recurrent graphs
论文作者
论文摘要
我们在无限图上研究了随机环境中的定向聚合物$ g =（v，e）$，基础随机步行在其上满足了频谱尺寸$ d_ {s} $严格少于两个小于两个。本文我们的目标是表明（i）淬火和退火的自由能$ f_q（β）$，$ f_a（β）$和（ii）的存在和巧合表明$ f_a（β）-f_q（β）-f_q（β）$可与$β^{\ frac {\ frac {\ frac {4} $ pobiote
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 $β$.
