论文标题
关于SLE和CLE相关的随机分形的自然测量
On Natural Measures of SLE- and CLE-Related Random Fractals
论文作者
论文摘要
在本文中，我们在几个随机分形上构造自然测量的唯一性，即SLE切割点，SLE边界接触点，CLE关键点和CLE地毯/垫圈。作为一种应用，我们还显示了本文定义的自然措施（即CLE PIVOTAL和GASKET措施）的等效性与在[Garban-Pete-Pete-Schramm，J。Amer中的关键连续性平面Bernoulli Percolation中的计数措施的离散类似物。数学。 Soc。，2013]。尽管在[Miller-Schoug，Arxiv：2201.01748]中已经证明了CLE地毯/垫圈的自然量度的存在和独特性，但在本文中，我们通过CLE和LQG的耦合提供了不同的论点。
In this paper, we construct and then prove the up-to constants uniqueness of the natural measure on several random fractals, namely the SLE cut points, SLE boundary touching points, CLE pivotal points and the CLE carpet/gasket. As an application, we also show the equivalence between our natural measures defined in this paper (i.e. CLE pivotal and gasket measures) and their discrete analogs of counting measures in critical continuum planar Bernoulli percolation in [Garban-Pete-Schramm, J. Amer. Math. Soc.,2013]. Although the existence and uniqueness for the natural measure for CLE carpet/gasket have already been proved in [Miller-Schoug, arXiv:2201.01748], in this paper we provide with a different argument via the coupling of CLE and LQG.
