论文标题
Galton-Watson树上的抛物线Anderson模型
The parabolic Anderson model on a Galton-Watson tree
论文作者
论文摘要
我们研究了具有有界度的超临界Galton-Watson随机树上抛物线安德森模型（PAM）的总质量的长期渐近造型。我们根据一个变异公式来确定对该渐近学的二阶贡献，该公式提供了有关浓缩溶液的局部结构的信息。该公式背后的分析表明，在模型参数的轻度条件下，浓度发生在最小程度的树上。我们的方法可以应用于有限的本地树状随机图，在时间和图形大小趋于无穷大的情况下，以耦合极限。例如，我们考虑配置模型，或更确切地说，具有规定度序列的均匀简单随机图。
We study the long-time asymptotics of the total mass of the solution to the parabolic Anderson model (PAM) on a supercritical Galton-Watson random tree with bounded degrees. We identify the second-order contribution to this asymptotics in terms of a variational formula that gives information about the local structure of the region where the solution is concentrated. The analysis behind this formula suggests that, under mild conditions on the model parameters, concentration takes place on a tree with minimal degree. Our approach can be applied to finite locally tree-like random graphs, in a coupled limit where both time and graph size tend to infinity. As an example, we consider the configuration model or, more precisely, the uniform simple random graph with a prescribed degree sequence.
