论文标题
带有大脸的双极导向的随机平面图和异国情调的SLE $_κ（ρ）$ processes
Bipolar oriented random planar maps with large faces and exotic SLE$_κ(ρ)$ processes
论文作者
论文摘要
我们认为具有重型面部度的双极导向的随机平面图。我们为（1,2）$中的每个$α\显示，如果面部度在吸引$α$稳定的lévy过程的领域，则相应的随机平面图在本杰米尼 - schramm拓扑结构中具有无限的体积限制。我们还表明，与西北和东南树相关的适当重新缩放的轮廓功能在法律上汇合到一对相关的$α$稳定的莱维工艺。再加上其他工作，这使我们能够使用SLE $_κ（ρ）$进程确定平面图的缩放限制，并在$ \sqrtκ$ -liouville量子重力上使用$ \sqrtκ$ -4 <-2 $ in（4/3,2）$α，$α，κ$ $α，κ$ y $α= 4/κ相关。
We consider bipolar oriented random planar maps with heavy-tailed face degrees. We show for each $α\in (1,2)$ that if the face degree is in the domain of attraction of an $α$-stable Lévy process, the corresponding random planar map has an infinite volume limit in the Benjamini-Schramm topology. We also show in the limit that the properly rescaled contour functions associated with the northwest and southeast trees converge in law to a certain correlated pair of $α$-stable Lévy processes. Combined with other work, this allows us to identify the scaling limit of the planar map with an SLE$_κ(ρ)$ process with $ρ= κ-4 < -2$ on $\sqrtκ$-Liouville quantum gravity for $κ\in (4/3,2)$ where $α, κ$ are related by $α= 4/κ-1$.
