论文标题
在具有顶点障碍的关键分层图上定向聚合物的弱端限
Weak-disorder limit for directed polymers on critical hierarchical graphs with vertex disorder
论文作者
论文摘要
我们研究了在随机环境（DPRE）中的定向聚合物模型，其中聚合物遍历分层钻石图，并且通过附着在顶点的随机变量来定义随机环境。对于这些模型，我们证明了分区函数的分布限制定理，在限制方向上，随着聚合物与随机环境的耦合，系统的生长被适当地减弱。钻石图的序列取决于\ {2,3，\ ldots \} $的分支数$ b \ in \ {2,3，\ ldots \} $的分支数量$ b \ in \ {2,3，\ ldots \} $确定，我们的重点是型号的关键情况，其中$ b = s $。这扩展了在类似模型的关键情况下的最新工作，该模型的变量位于图形边缘而不是顶点。
We study models for a directed polymer in a random environment (DPRE) in which the polymer traverses a hierarchical diamond graph and the random environment is defined through random variables attached to the vertices. For these models, we prove a distributional limit theorem for the partition function in a limiting regime wherein the system grows as the coupling of the polymer to the random environment is appropriately attenuated. The sequence of diamond graphs is determined by a choice of a branching number $b\in \{2,3,\ldots\}$ and segmenting number $s\in \{2,3,\ldots\}$, and our focus is on the critical case of the model where $b=s$. This extends recent work in the critical case of analogous models with disorder variables placed at the edges of the graphs rather than the vertices.
