论文标题
自相似的随机结构定义为分布方程的固定点
Self-similar random structures defined as fixed points of distributional equations
论文作者
论文摘要
我们考虑在测得的度量空间等轴测类别上的概率分布的定点方程。构造必须具有递归和树状，但是我们允许在衡量标准的点之间进行测量学的循环：一个人可以想到一个绕一个循环分解的$β$稳定的循环。我们通过迭代研究解决方案的存在和独特性，以及固定点的吸引力。我们获得了Hausdorff和上Minkowski尺寸的边界，对于研究模型而言，它们似乎很紧。该设置适用于以前研究的结构，作为$β$稳定的树木和循环，我们给出了新的特征并恢复分形维度。
We consider fixed-point equations for probability distributions on isometry classes of measured metric spaces. The construction is required to be recursive and tree-like, but we allow loops for the geodesics between points in the support of the measure: one can think of a $β$-stable looptree decomposed around one loop. We study existence and uniqueness of solutions together with the attractiveness of the fixed-points by iterating. We obtain bounds on the Hausdorff and upper Minkowski dimension, which appear to be tight for the studied models. This setup applies to formerly studied structures as the $β$-stable trees and looptrees, of which we give a new characterization and recover the fractal dimensions.
