论文标题
Looptree，Fennec和ICRT的蛇
Looptree, Fennec, and Snake of ICRT
论文作者
论文摘要
我们介绍了一种新的平面$ \ mathbb r $ -tree理论，以定义平面iCrt（不均匀的连续性随机树），其循环树（Looptree上的高斯免费场）和蛇。我们证明了A.S. Looptree紧凑，A.S.芬内克和蛇是连续的。我们计算Looptree的分形维度，以及Fennec和Snake的Hölder指数。在旁边，我们在ICRT上定义了高斯自由场，并证明了其连续性的条件。在同伴论文中，我们证明具有固定度序列的树木，fennecs和蛇的蛇会收敛于ICRT的循环，Fennecs和蛇。
We introduce a new theory of plane $\mathbb R$-tree, to define plane ICRT (inhomogeneous continuum random tree), and its looptree, fennec (a Gaussian free field on the looptree), and snake. We prove that a.s. the looptree is compact, and that a.s. the fennec and snake are continuous. We compute the looptree's fractal dimensions, and the fennec and snake's Hölder exponent. Alongside, we define a Gaussian free field on the ICRT, and prove a condition for its continuity. In a companion paper , we prove that the looptrees, fennecs, and snakes of trees with fixed degree sequence converge toward the looptrees, fennecs and snakes of ICRT.
