论文标题
在随机树上停车的相过渡的清晰度
Sharpness of the phase transition for parking on random trees
论文作者
论文摘要
最近，已经建立了一种用于在随机树上停车的现象。我们将Curien和Hénard的结果扩展到Galton将军 - Watson Trees，并根据顶点超高剂允许不同的汽车到达分布。然后，我们通过建立出退出汽车的通量来证明这种相转换是急剧的。这对停放的斑点的远距离几何形状产生了影响，该几何形状显示出与经典的Erdős-Renyi随机图模型的相似之处。
Recently, a phase transition phenomenon has been established for parking on random trees. We extend the results of Curien and Hénard on general Galton--Watson trees and allow different car arrival distributions depending on the vertex outdegrees. We then prove that this phase transition is sharp by establishing a large deviations result for the flux of exiting cars. This has consequences on the offcritical geometry of clusters of parked spots which displays similarities with the classical Erdős-Renyi random graph model.
