论文标题
无限图上的定向聚合物
Directed polymers on infinite graphs
论文作者
论文摘要
我们研究了用于通用图（超过$ \ Mathbb Z^d $）和随机步行的定向聚合物模型。在图和随机步行的性质方面，我们为弱混乱阶段的存在或不存在非常强大的疾病提供了足够的条件。我们在包括Galton Watson树在内的各种树木上进行一些详细研究（有偏见）随机步行，并提供了一系列示例，这些例子说明了反述$ \ Mathbb Z^d $/srw结果的直观扩展。
We study the directed polymer model for general graphs (beyond $\mathbb Z^d$) and random walks. We provide sufficient conditions for the existence or non-existence of a weak disorder phase, of an $L^2$ region, and of very strong disorder, in terms of properties of the graph and of the random walk. We study in some detail (biased) random walk on various trees including the Galton Watson trees, and provide a range of other examples that illustrate counter-examples to intuitive extensions of the $\mathbb Z^d$/SRW result.
