Probability laws for the distribution of geometric lengths when sampling by a random walk in a Fuchsian fundamental group
Probability laws for the distribution of geometric lengths when sampling by a random walk in a Fuchsian fundamental group
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Fuchsian 基本群中随机游走采样时几何长度分布的概率定律
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
Peter S Park
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文献类型：
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作者：
Peter S Park
设$S=Gammaackslash Mathbb{H}$是有限拓扑型双曲曲面，使得Fuchsian群$Gamma le算子名{PSL}_2(Mathbb{R})$是非初等的.我们证明了存在一个$Mathfrak S$生成集，满足如下条件：当在$pi_1(S)从Gamma$中的一个元素每给出一个步长，用一个$n$步的随机游动进行抽样时，这个由双曲元素组成的抽样集子集逼近完全测度为$n，并且对于这个子集，几何长度的分布服从大数定律、中心极限定理、大偏差原理和局部极限定理。
Let $S=Gammaackslash mathbb{H}$ be a hyperbolic surface of finite topological type, such that the Fuchsian group $Gamma le operatorname{PSL}_2(mathbb{R})$ is non-elementary. We prove that there exists a generating set $mathfrak S$ of $Gamma$ satisfying the following: when sampling by an $n$-step random walk in $pi_1(S) cong Gamma$ with each step given by an element in $mathfrak S$, the subset of this sampled set comprised of hyperbolic elements approaches full measure as $n o infty$, and for this subset, the distribution of geometric lengths obeys a Law of Large Numbers, Central Limit Theorem, Large Deviations Principle, and Local Limit Theorem.
随机闭合测地线的中心极限定理：Chas-Li-Maskit 猜想的证明
影响因子：
1.7
作者：
Gekhtman, Ilya;Taylor, Samuel J.;Tiozzo, Giulio
通讯作者：
Tiozzo, Giulio